Home Zagreb Polynomials and redefined Zagreb indices of Dendrimers and Polyomino Chains
Article Open Access

Zagreb Polynomials and redefined Zagreb indices of Dendrimers and Polyomino Chains

  • Adeel Farooq , Mustafa Habib , Abid Mahboob , Waqas Nazeer and Shin Min Kang EMAIL logo
Published/Copyright: December 31, 2019
Download Article (PDF)
Open Chemistry
From the journal Open Chemistry Volume 17 Issue 1

Abstract

Dendrimers have an incredibly strong potential because their structure allows multivalent frameworks, i.e. one dendrimer molecule has many possible destinations to couple to a functioning species. Researchers expected to utilize the hydrophobic conditions of the dendritic media to lead photochemical responses that make the things that are artificially tested. Carboxylic acid and phenol- terminated water-dissolvable dendrimers were joined to set up their utility in tranquilize conveyance and furthermore driving compound reactions in their inner parts. This may empower scientists to associate both concentrating on atoms and medication particles to the equivalent dendrimer, which could diminish negative manifestations of prescriptions on sound and health cells. Topological indices are numerical numbers associated with the graphs of dendrimers and are invariant up to graph isomorphism. These numbers compare certain physicochemical properties like boiling point, strain energy, stability, etc. of a synthetic compound. There are three main types of topological indices, i.e degree-based, distance-based and spectrum-based. In this paper, our aim is to compute some degree-based indices and polynomials for some dendrimers and polyomino chains. We computed redefined first, second and third Zagreb indices of PAMAM dendrimers PD1, PD2, and DS1 and linear Polyomino chain Ln , Zigzag Polyomino chain Zn, polyomino chain with n squares and of m segments Bn1and Bn2We also computed some Zagreb polynomials of understudy dendrimers and chains.

Keywords: Zagreb Index; Zagreb Polynomial; Dendrimers; Polyomino chain; Chemical graph theory

1 Introduction

In medicine mathematical modelling is used to understand the structure of new drugs, usually as an undirected graph where each vertex exhibits a molecule and each edge addresses a bond between atoms. A huge number of new drugs are made each year which then requires significant work to choose the pharmacological, compound and organic qualities of these new drugs. This is challenging for countries, in for example South America, Southeast Asia, Africa and India where the cost for gauging the biochemical properties is prohibitive.

It has been proven in numerous studies that there is a strong link between the properties of compounds and drugs with their molecular structure. The topological index (TI) defined on the structure of these compounds can help researchers to develop an understanding of the physical characteristics, chemical reactivity and biological activity [1,2]. Therefore, the study of TIs of chemical structures of drugs can provide a theoretical basis for the preparation of new drugs [3].

In the past two decades many TIs have been defined and used in toxicology, environmental chemistry, pharmacology and theoretical chemistry [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14].

The oldest degree-based TIs were defined by Gutman in [14] and are known by different names such as Sag. Loeb group parameters, Zagreb group index. Nowadays these indices are known as first Zagreb index and second Zagreb index. Zagreb indices are used to studying chirality, heterogeneity, ZE isomers and molecular complexity and have potential relevance with multiple linear regression models. For detailed survey we refer to [14, 15, 16, 17].

The Polyomino Chains is a finite 2-connected floor plan, where each inner face (or a unit) is encompassed by a square of length one. It is a union of cells connected by edges in a planar square lattice [18, 19, 20]:

Dendrimer originates from the Greek word meaning “trees” [21,22] and are redundantly spread molecules. Dendrimers are commonly symmetrical about the center and generally display a circular three-dimensional morphology. The first dendrimer was made by Fritz Vögtle in [23] utilizing distinctive engineered techniques RG Denkewalter in Allied in [24,25] Donald Tomalia in Dow Chemical in [26] and [27,28] and in [29] by George R. Newkome 1990, Craig Hawker and Jean Fréchet presented a combination union strategy. The prevalence of dendrimers has significantly expanded and y 2005 there were in excess of 5,000 logical papers and patents. We aim to study some Zagreb polynomials and redefined Zagreb indices of Polyomino Chains and Dendrimers in this paper.

2 Basic Notions

In this section, we will give some definitions and basic theory of chemical graph theory.

Throughout this paper G means a connected simple graph, V(G) and E(G) represent the vertex set and edge set of G respectively. The degree of a vertex v ∈ V( G) is the number of vertices attached to it. The formulae for the first and second Zagreb indices are (cf. [14])

M1(G)=∑uv∈E(G) (du+dv)

and

M2(G)=∑uvE(G) (du×dv).

After the success of Zagreb indices, the following first and second Zagreb polynomials were introduced [30]

M1(G,x)=∑uv∈E(G) xdu+dv

and

M2(G,x)=∑uv∈E(G) xdu⋅dv.

These Zagreb polynomials fund applications in chemistry due to their symmetric behaviour [31].

The third Zagreb index is defined as [32]

M3(G)=∑uv∈E(G) |du−dv|.

and the third Zagreb polynomial is defined as:

M3(G,x)=    ∑uv∈E(G) x|du−dv|.

Bindusree et al. [33] defined the following Zagreb type polynomials.

M4(G,x)=∑uv∈E(G) xdu(dn+dv)M5(G,x)=∑uv∈E(G) xdv(du+dv)Ma,b(G,x)=∑uv∈E(G) xadu+bdvMa,b'(G,x)=∑uv∈E(G) x(du+a)(dv+b).

The first, second and third redefined Zagreb indices were defined by Ranjini et al. in [34]. These indicators appear as

ReZG1G=∑uv∈EPD1du+dvdu⋅dvReZG2G=∑uv∈EPD1du⋅dvdu+dvRe⁡ZG3G=∑uv∈EPD1du⋅dvdu+dv.

3 Main Results

3.1 Zagreb Polynomials and Redefined Zagreb indices of PAMAM Dendrimers

Polyamidoamine (PAMAM) dendrimers are hyperbranched polymers with unparalleled sub-atomic consistency, subatomic weight distribution, characterized size and shape qualities and a multifunctional terminal surface. These nanoscale polymers comprise an ethylenediamine center, a redundant fanning amidoamine inward structure and an essential amine terminal surface. Dendrimers are “grown” off a central core in an iterative assembling process, with each resulting venture speaking to another “generation” of dendrimer. Expanding generation (atomic weight) produce bigger sub-atomic measurements, double the quantity of responsive surface destinations, and around twofold the sub-atomic load of the first era. PAMAM dendrimers likewise expect a spheroidal, globular shape at Generation 4 or above. Their usefulness is promptly custom fitted, and their consistency, measure and profoundly responsive “sub-atomic Velcro” surfaces is keys to their utilization. Here we study PD1 which is PAMAM dendrimers with trifunctional center unit created by Gn dendrimer with n growth stages and the PAMAM dendrimers PD2 with various centers produced by dendrimer generators with n growth stages. DS1 is PAMAM dendrimers with n growth stages. The M-polynomials, first and second Zagreb indices, modified Zagreb index, generalized Randic index, inverse Randic index, symmetric division index, harmonic index, inverse sum index and augmented Zagreb index for some dendrimers and Polyomino chains were computed in [35]. In this paper we aim to compute Zagreb polynomials and redefined Zagreb indices of the same structures that were previously studied in [35].

Theorem 1

For the PAMAM dendrimers PD1, we have

  1. M3(PD1,x)=9(2n+1−1)+3(2n+3−4)x−1+3(2n+1−1)x−2.

  2. M4(PD1,x)=3.2nx3+3(2n+1−1)x4+9(2n+1−1)x8+3(7.2n−4)x10.

  3. M5(PD1,x)=3.2nx6+3(2n+1−1)x12+9(2n+1−1)x8+3(7.2n−4)x15.

  4.    Ma,b(PD1,x)=3(3⋅2n−1)xa+3(13⋅2n−7)x2a++3(7⋅2n−3)x2b+3(9⋅2n−5)x3b.

  5.   Ma,b'(PD1,x)=3.2nx(1+a)(1+b)+3(2n+1−1)x(1+a)(3+b)++9(2n+1−1)x(2+a)(2+b)+3(7⋅2n−4)x(2+a)(3+b).

Proof

The edge set of the molecular graph of PD1 PAMAM dendrimers has the following four classes depending on the degrees of end vertices.

E{1,2}={uv∈E(PD1)|du=1,dv=2},E{1,3}={uv∈E(PD1)|du=1,dv=3},E{2,2}={uv∈E(PD1)|du=2,dv=2},E{2,3}={uv∈E(PD1)|du=2,dv=3}.

Now

 |E{1,2}|=3.2n,|E{1,3}|=6.2n−3,|E{2,2}|=18⋅2n−9,

And

|E{2,3}|=21⋅2n−12.

  1. M3(PD1,x)=∑uv∈E(PD1) xdu−dv                           =∑uv∈E{1,2}(PD1) x1−2+∑uv∈E{1,3}(PD1) x1−3+∑uv∈E{2,2}(PD1) x2−2+∑uv∈E{2,3}(PD1) x2−3                           =|E{1,2}(PD1)|x−1+|E{1,3}(PD1)|x−2+|E{2,2}(PD1)|x0+|E{2,3}(PD1)|x−1                           =9(2n+1−1)+3(2n+3−4)x−1+3(2n+1−1)x−2.

  2. M3PD1,x=∑uv∈EPD1xdudu−dv=∑uv∈E1,2PD1x3+∑uv∈E1,3PD1x4+∑uv∈E2,2PD1x8+∑uv∈E2,3PD1x10=E1,2PD1x3+E1,3PD1x4+E2,2PD1x8+E2,3PD1x10=3⋅2nx3+32n+1−1x4+92n+1−1x8+37⋅2n−4x10.

  3. M3(PD1,x)=∑uv∈E(PD1)xdv(du−dv)=∑uv∈E{1,2}(PD1)x6+∑uv∈E{1,3}(PD1)x12+∑uv∈E{2,2}(PD1)x8+∑uv∈E{2,3}(PD1)x15=|E{1,2}(PD1)|x6+|E{1,3}(PD1)|x12+|E{2,2}(PD1)|x8+|E{2,3}(PD1)|x15=3⋅2nx6+3(2n+1−1)x12+9(2n+1−1)x8+3(7⋅2n−4)x15.

  4. Ma,b(PD1,x)=∑uv∈E(PD1)x(adu+bdv)=∑uv∈E{1,2}(PD1)xa+2b+∑uv∈E{1,3}(PD1)xa+3b+∑uv∈E{2,2}(PD1)x2a+2b+∑uv∈E{2,3}(PD1)x2a+3b=|E{1,2}(PD1)|xa+2b+|E{1,3}(PD1)|xa+3b+|E{2,2}(PD1)|x2a+2b+|E{2,3}(PD1)|x2a+3b=3(3⋅2n−1)xa+3(13⋅2n−7)x2a+3(7⋅2n−3)x2b+3(9⋅2n−5)x3b.

  5. Ma,b′PD1,x=∑uv∈EPD1xdu+adv+b=∑uv∈E1,2PD1x1+a2+b+∑uv∈E1,3PD1x1+a3+b+∑uv∈E2,2PD1x2+a2+b+∑uv∈E2,3PD1x2+a3+b=E1,2PD1x1+a2+b+E1,3PD1x1+a3+b+E2,2PD1x2+a+2+b+E2,3PD1x2+a+3+b=3⋅2nx1+a2+b+32n+1−1x1+a3+b+92n+1−1x2+a2+b+37⋅2n−4x2+a3+b.

Theorem 2

For the PAMAM dendrimers PD1 , we have

  1. Re ZG1(PD1)=3.2n+4−23.

  2. Re ZG2(PD2)=(49710)2n−51320.

  3. Re ZG3(PD1)=9(7⋅2n−60).

Proof

From the edge partition given in Theorem 1, we have

  1. ReZG1(PD1)=∑uv∈E(PD1) du+dvdu⋅dv                               =∑uv∈E{1,2}(PD1) 1+21⋅2+∑uv∈E{1,3}(PD1) 1+31⋅3+∑uv∈E{2,2}(PD1) 2+22⋅2+∑uv∈E{2,3}(PD1) 2+32⋅3                               =|E{1,2}(PD1)|32+|E{1,3}(PD1)|43+|E{2,2}(PD1)|44+|E{2,3}(PD1)|56                                =3⋅2n+4−23.

  2. Re⁡ZG2PD1=∑uv∈EPD1du⋅dvdu⋅dv=∑uv∈E1,2PD11⋅21+2+∑uv∈E1,3PD11⋅31+3+∑uv∈E2,2PD12⋅22+2+∑uv∈E2,3PD12⋅32+3=E1,2PD123+E1,3PD134+E2,2PD144+E2,3PD165=497102n−51320.

  3. ReZG2(PD1)=∑uv∈E(PD1)du⋅dvdu⋅dv        =∑uv∈E{1,2}(PD1)(1⋅2)(1+2)+∑uv∈E{1,3}(PD1)(1⋅3)(1+3)+∑uv∈E{2,2}(PD1)(2⋅2)(2+2)+∑uv∈E{2,3}(PD1)(2⋅3)(2+3)        =6|E{1,2}(PD1)|+12|E{1,3}(PD1)|+16|E{2,2}(PD1)|+30|E{2,3}(PD1)|        =9(7⋅2n−60).

Theorem 3

For the PAMAM dendrimers PD2 , we have

  1. M3(PD2,)x=(3⋅2n+3−11)+(2n+5−14)x−1+4(2n+1−1)x−2.

  2. M4(PD2,x)=2n+2x3+4(2n+1−1)+(24⋅2n−11)x8+14(2n+1−1)x10.

  3. M5(PD2,x)=2n+2x6+4(2n+1−1)x12+(24⋅2n−11)x8+14(2n+1−1)x15.

  4.        Ma,b(PD2,x)=4(3⋅2n−1)xa+(13⋅2n+2−25)x2a++(7⋅2n+2−11)x2b+18(2n+1−1)x3b.

  5.      Ma,b'(PD2,x)=2n+2x(1+a)(1+b)+4(2n+1−1)x(1+a)(3+b)++(24⋅2n−11)x(2+a)(2+b)+14(2n+1−1)x(2+a)(3+b).

Proof

The edge set of the molecular graph of PD2 PAMAM dendrimers can be divided into the following four types by mean of degree of end vertices.

E{1,2}={uv∈E(PD2)|du=1,dv=2},E{1,3}={uv∈E(PD2)|du=1,dv=3},E{2,2}={uv∈E(PD2)|du=2,dv=2},E{2,3}={uv∈E(PD2)|du=2,dv=3}.

Now

   |E{1,2}|=4⋅2n, |E{1,3}|=8⋅2n−4,|E{2,2}|=24⋅2n−11,               And|E{2,3}|=28⋅2n−14.

The remaining proof of our results follows similarly as in Theorem 1.

Theorem 4

For the PAMAM dendrimers PD2 , we have

  1. Re ZG1(PD2)=4(2n+4−7).

  2. Re ZG2(PD2)=(49715)2n+1−1545.

  3. Re ZG3(PD2)=7(3⋅2n+6−92).

Proof

Using the edge partition given in theorem 3 and definitions of the first, second and third redefined Zagreb indices, we get our desired results as in theorem 2.

Theorem 5

For the PAMAM dendrimers DS1 , we have

  1. M3(DS1,x)=10(3n−1)+4(3n−1)x−2+4⋅3nx−3.

  2. M4(DS1,x)=4⋅3nx5+10(3n−1)x8+4(3n−1)x12.

  3. M5(DS1,x)=10(3n−1)x8+4⋅3nx20+4(3n−1)x24.

  4. Ma,b(DS1,x)=4.3nxa+14(3n−1)x2a+10(3n−1)x2b+4(2⋅3−1)x4b.

  5. Ma,b'(DS1,x)=4⋅3nx(1+a)(4+b)+10(3n−1)x(2+a)(2+b)+4(3n−1)x(2+a)(4+b).

Proof

The edge set of the molecular graph of DS1 PAMAM dendrimers can be divided into the following three classes,

E{1,4}={uv ∈ E(DS1)|du=1,dv=4},E{2,2}={uv ∈ E(DS1)|du=2,dv=2},E{2,4}={uv ∈ E(DS1)|du=2,dv=4}.

Now

  |E{1,4}|=4⋅3n,|E{2,2}|=10⋅3n−10,

And

|E{2,4}|=4⋅3n−4.

The remaining proof follows directly as in Theorem 1.

Theorem 6

For the PAMAM dendrimers DS1 , we have

  1. Re ZG1(DS1)=18⋅3n−13.

  2. Re ZG2(DS1)=(27815)3n−463.

  3. Re ZG3(DS1)=16(3n+3−22).

3.2 Zagreb Polynomials and Redefined Zagreb indices of Polyomino Chains

The Polyomino system is a finite graph which is 2-connected plane in which each inner cell is encircled by a square. In simple words, the Polyomino system is an edge-connected union of cells within the planar square lattice. Polyomino chain is an example of Polyomino system [35].

Let Bn be the Polyomino chains having n squares. There exist 2n+1 number of edges in every Bn ∈Bn , where Bn is a linear chain and is denoted by Ln in the subgraph of Bn formed by the vertices having d(v)=3 is the molecular graph with exactly n-2 squares. Also, Bn can be called a zigzag chain and labelled as Z n if the subgraph of Bn is induced by the vertices with d(v)>2 is Pn .

The link of Polyomino chain is angularly connected squares. The segment of Polyomino chain can be defined as the maximum linear chain in the Polyomino chains. Let l(S) denote the length of S which is equal to the number of squares contains in S. For any segment S of a Polyomino chain, we have l(S) ∈ {2,3,4,..,n} . Moreover, we deduce l1 = n and m=1 for a linear chain Ln having n squares and li = 2 and m=n-1 for a zigzag chain Zn having n squares.

From now to onward, we consider that the Polyomino chain consists of a sequence of segments S1 ,S2 ,S3 ,...Sn and L(Si) = li , where m ≥ 1 and i ∈ {2,3,4,...,m} . We derive that

∑i=1mli=n+m−1.

Theorem 7

For a linear Polyomino chain Ln ,we have

  1. M3(Ln,x)=3(n−1)+4x−1.

  2. M4(Ln,x)=2x8+4x10+(3n−5)x18.

  3. M5(Ln,x)=2x8+4x15+4x15+(3n−5)x18.

  4. Ma,b(Ln,x)=6x2a+2x2b+(3n−5)x3a+(3n−1)x3b.

  5. Ma,b'(Ln,x)=2x(2+a)(2+b)+4x(2+a)(3+b)+(3n−5)x(3+a)(3+b).

Proof

Let Ln be the Polyomino chain with n squares where l1= n and m=1. Ln is called the linear chain.

The edge set of Ln Polyomino chain can be divided into following three classes

E{2,2}={e=uv∈E(Ln)|du=2,dv=2},E{2,3}={e=uv∈E(Ln)|du=2,dv=3},E{3,3}={e=uv∈E(Ln)|du=3,dv=3},

Now

   |E{2,2}|=2,|E{2,3}|=4,|E{3,3}|=3n−5.

The remaining proof is similar to Theorem 1.

Theorem 8

For a linear Polyomino chain Ln , we have

  1. Re Z1G(Ln)=2(n+1)

  2. Re ZG2(Ln)=92n−710.

  3. Re ZG3(Ln)=2(81n−59).

Theorem 9

For the Zigzag Polyomino chain Zn for n ≥ 2 , we have

  1. M3(Zn,x)=(3n−2m−3)+6x−1+2(m−1)x−2.

  2. M4(Zn,x)=2x8+4x10+2(m−1)x12+2x21+(3n−2m−5)x32.

  3. M5(Zn,x)=2x8+4x15+2(m−1)x24+2x28+(3n−2m−5)x32.

  4.   Ma,b(Zn,x)=2(m+2)x2a+2x2b+2x3a+4x3b++(3n−2m−5)x4a+(3n−5)x4b.

  5.    Ma,b'(Zn,x)=2x(2+a)(2+b)+4x(2+a)(3+b)+2(m−1)x(2+a)(4+b)++2x(3+a)(4+b)+(3n−2m−5)x(4+a)(4+b).

Proof

Let Zn be zigzag Polyomino chain with n squares such that li = 2 and m = n -1 .Polyomino chain consists of a sequence of segments S1 , S2 ,...Sm and l (Si) = li where m≥1 and i ∈ {1,2,...,m}.

The edge set of Zn has following five partitions,

E{2,2}={e=uv∈E(Zn)|du=2,dv=2},E{2,3}={e=uv∈E(Zn)|du=2,dv=3},
E{2,4}={e=uv∈E(Zn)|du=2,dv=4},E{3,4}={e=uv∈E(Zn)|du=3,dv=4},E{4,4}={e=uv∈E(Zn)|du=4,dv=4}.

Now

   |E{2,2}|=2,   |E{2,3}|=4,|E{2,4}|=2(m−1),     |E{3,4}|=2,

And

|E{4,4}|=3n−2n−5.

Theorem 10

For the Zigzag Polyomino chain Zn for n ≥ 2 , we have

  1. Re ZG1(Zn)=32n+12m+52

  2. Re ZG2(Zn)=6n−43m−256105.

  3. Re ZG3(Zn)=32(12n−5m−13).

Theorem 11

For the Polyomino chain with n squares and of m segments S1 and S2 satisfy l1 = 2 and l2 = n −1, Bn1(n≥3), we have

  1. M3(Bn1,x)=(3n−8)+8x−1+x−2.

  2. M4(Bn1,x)=2x8+5x10+x12+(3n−10)x28+3x21.

  3. M5(Bn1,x)=2x8+5x15+x24+(3n−10)x18+3x28.

  4. Ma,b(Bn1,x)=8x2a+2x2b+(3n−7)x3a+(3n−5)x3b+4x4b.

  5.      Ma,b'(Bn1,x)=2x(2+a)(2+b)+5x(2+a)(3+b)+x(2+a)(4+b)++(3n−10)x(3+a)(3+b)+3x(3+a)(4+b).

Proof

Let Bn1(n≥3)be the Polyomino chain with n squares and of m segments S1 and S2 satisfy l1 = 2 and l2 = n −1 .The edge set of Bn1(n≥3)has following five partitions,

E{2,2}={e=uv∈E(Bn1)|du=2,dv=2},E{2,3}={e=uv∈E(Bn1)|du=2,dv=3},E{2,4}={e=uv∈E(Bn1)|du=2,dv=4},E{3,3}={e=uv∈E(Bn1)|du=3,dv=3},E{3,4}={e=uv∈E(Bn1)|du=3,dv=4}.

Now

|E{2,2}|=2,|E{2,3}|=5,|E{2,4}|=1,|E{3,3}|=3n−10,|E{3,4}|=3.and

Theorem 12

For the Polyomino chain with n squares and of m segments S1 and S2 satisfy l1 = 2 and l2 = n −1, Bn1(n≥3), we have

  1. ReZG1(Bn1)=2(n+1)

  2. ReZG2(Bn1)=92n−10721.

  3. Re ZG3(Bn1)=2(81n−29).

Theorem 13

For Polyomino chain with n squares and m segments S1,S2,...,Sm (m≥3) satisfy l1 = lm = 2 and l2,...,lm-1 ≥ 3 , Bn2(n≥4), we have

  1. M3(Bn2,x)=(3n−6m+1)+6(m−1)x−1+2x−2.

  2. M4(Bn2,x)=2x8+2mx10+2x12+3(n−2m+1)x18+2(2m−3)x21.

  3. M5(Bn2,x)=2x8+2mx15+2x24+3(n−2m+1)x18+2(2m−3)x28.

  4.      Ma,b(Bn2,x)=2(m+2)x2a+2x2b+(3n−2m−3)x3a++(3n−4m+3)x3b+4(m−1)x4b.

  5.      M′a,b(Bn2,x)=2x(2+a)(2+b)+2mx(2+a)(2+b)+2x(2+a)(2+b)++(3n−6m+3)x(3+a)(3+b)+2(2m−3)x(3+a)(4+b).

Proof

Let Bn2(n≥4)be a Polyomino chain with n squares and m segments S1 , S2 ,..., Sm (m≥ 3) satisfy l1 = lm = 2 and l2 ,...,l m-1 ≥ 3 . Then the edge set of Bn2(n≥4)has following five partitions,

E{2,2}={e=uv∈E(Bn2)|du=2,dv=2},E{2,3}=n{e=uv∈E(Bn2)|du=2,dv=3},E{2,4}={e=uv∈E(Bn2)|du=2,dv=4},E{3,3}={e=uv∈E(Bn2)|du=3,dv=3},E{3,4}={e=uv∈E(Bn2)|du=3,dv=4}.

Now

|E{2,2}|=2,|E{2,3}|=2m,|E{2,4}|=2,|E{3,3}|=3n−6m+3,

And

|E{4,4}|=4m−6.

Theorem 14

For Polyomino chain with n squares and m segments S1 , S2,..., Sm (m≥ 3) satisfy l1 = lm = 2 and l2 ,...,l m-1 ≥ 3 , Bn2(n≥4), we have

  1. ReZG1(Bn2)=2(n+1)

  2. ReZG2(Bn2)=92n+935m−4742.

  3. ReZG3(Bn2)=2(81n+36m−107).

4 Conclusion

Dendrimers are polymeric materials that given its structure in the form of branched molecules can benefit of mathematical arguments such as Polyomino chains, making this manuscript highly relevant for this type of molecules [36,37]. It is important to calculate topological indices of dendrimers, because it is proven fact that topological indices help to predict many properties without requiring experimental work. For example, the first and second Zagreb indices were found to happen for the calculation of the π-electron energy of dendrimers, the Randic index corresponds with boiling point, the atomic bond connectivity (ABC) index gives an exceptionally decent relationship to understanding the strain energy of dendrimers and augmented Zagreb index is a good tool to predict the heat of formation of dendrimers, etc. There are round about 148 topological indices [38, 39, 40] but none of them can completely describe all properties of a chemical compound. Therefore there is always room to define and study new topological indices. Redefined Zagreb indices are one step in this direction and are very close to Zagreb indices. Zagreb indices are very well studied by chemists and mathematician due to its huge applications in chemistry [41]. In this paper, we calculated first, second and third redefined Zagreb indices for of PAMAM dendrimers PD1, PD2 , and DS1 and linear Polyomino chain Ln , Zigzag Polyomino chain Zn , polyomino chain with n squares and of m segments Bn1 and Bn2. We also computed Zagreb polynomials for the above mentioned dendrimers and Polyomino chains. Our results together with QSPR and QSAR can predict properties of understudy materials and are helpful in formulation of new drugs. It is interesting to compute distance-based indices and polynomials for the materials studied in this paper.

  1. Ethical approval: The conducted research is not related to either human or animal use.

  2. Conflict of interest: Authors declare no conflict of interest.

References

[1] Devillers J., Balaban A.T., Topological indices and related descriptors in QSAR and QSPAR. CRC Press, 2000.10.1201/9781482296945Search in Google Scholar

[2] Balaban A.T., Motoc I., Bonchev D., Mekenyan O., Topological indices for structure-activity correlations. In Steric effects in drug design, Springer, Berlin, Heidelberg 1983, pp. 21-55.10.1007/BFb0111212Search in Google Scholar

[3] Estrada E., Uriarte E., Recent advances on the role of topological indices in drug discovery research, Current Medicinal Chemistry, 2001, 8(13), 1573-1588.10.2174/0929867013371923Search in Google Scholar PubMed

[4] Alaeiyan M., Farahani M.R., Jamil M.K., Computation of the fifth geometric-arithmetic index for polycyclic aromatic hydrocarbons PaHk, Applied Mathematics and Nonlinear Sciences, 2016, 1(1), 283-290.10.21042/AMNS.2016.1.00023Search in Google Scholar

[5] Jamil M.K., Farahani M.R., Imran M., Malik M.A., Computing eccentric version of second zagreb index of polycyclic aromatic hydrocarbons PAHk. Applied Mathematics and Nonlinear Sciences, 2016, 1(1), 247-252.10.21042/AMNS.2016.1.00019Search in Google Scholar

[6] Farahani M.R., Jamil M.K., Imran M., Vertex PIv topological index of titania carbon nanotubes TiO2 (m, n), Appl. Math. Nonl. Sc, 2016, 1(1), 175-182.10.21042/AMNS.2016.1.00013Search in Google Scholar

[7] Gao W., Zali M.R., Degree-based indices computation for special chemical molecular structures using edge dividing method, Applied Mathematics and Nonlinear Sciences, 2016,1(1), 94-117.10.21042/AMNS.2016.1.00009Search in Google Scholar

[8] Basavanagoud B., Gao W., Patil S., Desai V.R., Mirajkar K.G., Balani P., Computing First Zagreb index and F-index of New C-products of Graphs, Applied Mathematics and Nonlinear Sciences, 2017, 2(1), 285-298.10.21042/AMNS.2017.1.00024Search in Google Scholar

[9] Lokesha V., Deepika T., Ranjini P.S., Cangul I.N., Operations of Nanostructures via SDD, ABC4 and GA5 indices, Applied Mathematics and Nonlinear Sciences, 2017, 2(1), 173-180.10.21042/AMNS.2017.1.00014Search in Google Scholar

[10] Hosamani S.M., Kulkarni B.B., Boli R.G., Gadag V.M., QSPR analysis of certain graph theocratical matrices and their corresponding energy, Applied Mathematics and Nonlinear Sciences, 2017, 2(1), 131-150.10.21042/AMNS.2017.1.00011Search in Google Scholar

[11] Sardar M.S., Zafar S., Zahid Z., Computing topological indices of the line graphs of Banana tree graph and Firecracker graph, Applied Mathematics and Nonlinear Sciences, 2017, 2(1), 83-92.10.21042/AMNS.2017.1.00007Search in Google Scholar

[12] Basavanagoud B., Desai V.R., Patil S., (β, α) connectivity index of graphs, Applied Mathematics and Nonlinear Sciences, 2017, 2(1), 21-30.10.21042/AMNS.2017.1.00003Search in Google Scholar

[13] Ramane H.S., Jummannaver R.B., Note on forgotten topological index of chemical structure in drugs, Applied Mathematics and Nonlinear Sciences, 2016, 1(2), 369-374.10.21042/AMNS.2016.2.00032Search in Google Scholar

[14] Gutman I., Das K.C., The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem, 2004, 50(1), 83-92.Search in Google Scholar

[15] Miličević A., Nikolić S., On variable Zagreb indices, Croatica chemica acta, 2004, 77(1-2), 97-101.Search in Google Scholar

[16] Bonche D., Trinajstič N., Overall molecular descriptors. 3. Overall Zagreb indices, SAR and QSAR in Environmental Research, 2001, 12(1-2), 213-236.10.1080/10629360108035379Search in Google Scholar PubMed

[17] Baja S., Sambi S.S., Madan A.K., Prediction of anti-inflammatory activity of N-arylanthranilic acids: computational approach using refined Zagreb indices, Croat Chem Acta, 2005, 78(2), 165-174.Search in Google Scholar

[18] Klarner D.A., Cell growth problems, Canad. J. Math., 1967, 19, 851-863.10.4153/CJM-1967-080-4Search in Google Scholar

[19] Golomb S.W., Polyominoes: puzzles, patterns, problems, and packings, Princeton University Press, 1996.Search in Google Scholar

[20] Alonso L., Cerf R., The three dimensional polyominoes of minimal area, The electronic journal of combinatorics, 1996, 3(1), R27.10.37236/1251Search in Google Scholar

[21] Astruc D., Boisselier E., Ornelas C., Dendrimers designed for functions: from physical, photophysical, and supramolecular properties to applications in sensing, catalysis, molecular electronics, photonics, and nanomedicine, Chemical reviews, 2010, 110(4), 1857-1959.10.1021/cr900327dSearch in Google Scholar PubMed

[22] Vögtle F., Richardt G., Werner N., Dendrimer chemistry: concepts, syntheses, properties, applications. John Wiley & Sons, 2009.ISBN 3-527-32066-010.1002/9783527626953Search in Google Scholar

[23] Hirsch B.E., Lee S., Qiao B., Chen C.H., McDonald K.P., Tait S.L., Flood A.H., Anion-induced dimerization of 5-fold symmetric cyanostars in 3D crystalline solids and 2D self-assembled crystals, Chemical Communications, 2014, 50(69), 9827-9830.10.1039/C4CC03725ASearch in Google Scholar PubMed

[24] Buhleier E., Wehner W., Vögtle F., Cascade- and Nonskid-Chain-like Syntheses of Molecular Cavity Topologies, Synthesis., 1978, 2, 155–158.10.1055/s-1978-24702Search in Google Scholar

[25] Denkewalter R.G., Kolc J., Lukasavage W.J., U.S. Patent No. 4,289,872. Washington, DC: U.S. Patent and Trademark Office, 1981.Search in Google Scholar

[26] Denkewalter R.G., Kolc J., Lukasavage W.J., U.S. Patent No. 4,289,872. Washington, DC: U.S. Patent and Trademark Office, 1981.Search in Google Scholar

[27] Tomalia D.A., Dewald J.R., U.S. Patent No. 4,507,466. Washington, DC: U.S. Patent and Trademark Office, 1985.Search in Google Scholar

[28] Tomalia D.A., Baker H., Dewald J., Hall M., Kallos G., Martin S., Roeck J., Ryder J., Smith P., A new class of polymers: starburst-dendritic macromolecules, Polymer Journal, 1985,17(1), p.117.10.1295/polymj.17.117Search in Google Scholar

[29] Donald A., Treelike molecules branch out. Tomalia synthesized first dendrimer molecule-chemistry-brief article, Sci. News,1996, 149, 17-32.Search in Google Scholar

[30] Fath-Tabar G.H., Old and new Zagreb index, MATCH-Commun. Math. Comput. Chem., 2011, 65, 79-84.Search in Google Scholar

[31] Gutman I., New bounds on zagreb indices and the zagreb co-indices, Bol Soc Paran Mat., 2013, 31(1), 51-5.10.5269/bspm.v31i1.15272Search in Google Scholar

[32] Fath-Tabar G.H., Zagreb Polynomial and Pi Indices of some Nano Structures, Digest Journal of Nanomaterials and Biostructures, 2009, 4(1), 189-191.Search in Google Scholar

[33] Bindusree A.R., Cangul I.N., Lokesha V., Cevik A.S., Zagreb polynomials of three graph operators, Filomat, 2016, 30(7), 1979-1986.10.2298/FIL1607979BSearch in Google Scholar

[34] Ranjini P.S., Lokesha V., Usha A., Relation between phenylene and hexagonal squeeze using harmonic index, Int J Graph Theory., 2013, 1, 116-121.Search in Google Scholar

[35] Kwun Y. C., Farooq A., Nazeer W., Zahid Z., Noreen S., Kang S.M., Computations of the M-Polynomials and Degree-Based Topological Indices for Dendrimers and Polyomino Chains. International, Journal of Analytical Chemistry, 2018, 2018, Article ID 1709073, pp. 11,10.1155/2018/1709073Search in Google Scholar PubMed PubMed Central

[36] Bosman D.A., Janssen H.M., Meijer E.W., About dendrimers: structure, physical properties, and applications, Chemical reviews, 1996, 99(7), 1665-1688.10.1021/cr970069ySearch in Google Scholar PubMed

[37] Noriega-Luna B., Godínez L.A., Rodríguez F.J., Rodríguez A., Larrea G., Sosa-Ferreyra C.F., Mercado-Curiel R.F., Manríquez J., Bustos E., Applications of dendrimers in drug delivery agents, diagnosis, therapy, and detection, Journal of Nanomaterials, 2014, p.39.10.1155/2014/507273Search in Google Scholar

[38] Kang S.M., Nazeer W., Gao W., Afzal D., Gillani S.N., M-Polynomials and Topological Indices of Dominating David Derived Networks, Open Chemistry, 2018, 16(1), 201-213.10.1515/chem-2018-0023Search in Google Scholar

[39] Ali A., Nazeer W., Munir M., Kang S.M., M-Polynomials And Topological Indices Of Zigzag And Rhombic Benzenoid Systems, Open Chemistry, 2018, 16(1), 73-78.10.1515/chem-2018-0010Search in Google Scholar

[40] Kang S.M., Zahid M.A., Nazeer W., Gao W., Calculating the Degree-based Topological Indices of Dendrimers, Open Chemistry, 2018, 16(1), 681-688.10.1515/chem-2018-0071Search in Google Scholar

[41] Lather V., Madan A.K., Topological models for the prediction of HIV-protease inhibitory activity of tetrahydropyrimidin-2-ones. Journal of Molecular Graphics and Modelling, 2005, 23(4), 339-345.10.1016/j.jmgm.2004.11.005Search in Google Scholar PubMed

Received: 2018-05-08
Accepted: 2018-09-14
Published Online: 2019-12-31

© 2019 Adeel Farooq et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 Public License.

Articles in the same Issue

  1. Regular Articles
  2. Research on correlation of compositions with oestrogenic activity of Cistanche based on LC/Q-TOF-MS/MS technology
  3. Efficacy of Pyrus elaeagnifolia subsp. elaeagnifolia in acetic acid–induced colitis model
  4. Anti-inflammatory and antinociceptive features of Bryonia alba L.: As a possible alternative in treating rheumatism
  5. High efficiency liposome fusion induced by reducing undesired membrane peptides interaction
  6. Prediction of the Blood-Brain Barrier Permeability Using RP-18 Thin Layer Chromatography
  7. Phytic Acid Extracted from Rice Bran as a Growth Promoter for Euglena gracilis
  8. Development of a validated spectrofluorimetric method for assay of sotalol hydrochloride in tablets and human plasma: application for stability-indicating studies
  9. Topological Indices of Hyaluronic Acid-Paclitaxel Conjugates’ Molecular Structure in Cancer Treatment
  10. Thermodynamic properties of the bubble growth process in a pool boiling of water-ethanol mixture two-component system
  11. Critical Roles of the PI3K-Akt-mTOR Signaling Pathway in Apoptosis and Autophagy of Astrocytes Induced by Methamphetamine
  12. Characteristics of Stable Hydrogen and Oxygen Isotopes of Soil Moisture under Different Land Use in Dry Hot Valley of Yuanmou
  13. Specific, highly sensitive and simple spectrofluorimetric method for quantification of daclatasvir in HCV human plasma patients and in tablets dosage form
  14. Chromium-modified cobalt molybdenum nitrides as catalysts for ammonia synthesis
  15. Langerhans cell-like dendritic cells treated with ginsenoside Rh2 regulate the differentiation of Th1 and Th2 cells in vivo
  16. Identification of Powdery Mildew Blumeria graminis f. sp. tritici Resistance Genes in Selected Wheat Varieties and Development of Multiplex PCR
  17. Computational Analysis of new Degree-based descriptors of oxide networks
  18. The Use Of Chemical Composition And Additives To Classify Petrol And Diesel Using Gas Chromatography–Mass Spectrometry And Chemometric Analysis: A Uk Study
  19. Minimal Energy Tree with 4 Branched Vertices
  20. Jatropha seed oil derived poly(esteramide-urethane)/ fumed silica nanocomposite coatings for corrosion protection
  21. Calculating topological indices of certain OTIS interconnection networks
  22. Energy storage analysis of R125 in UIO-66 and MOF-5 nanoparticles: A molecular simulation study
  23. Velvet Antler compounds targeting major cell signaling pathways in osteosarcoma - a new insight into mediating the process of invasion and metastasis in OS
  24. Effects of Azadirachta Indica Leaf Extract, Capping Agents, on the Synthesis of Pure And Cu Doped ZnO-Nanoparticles: A Green Approach and Microbial Activity
  25. Aqueous Micro-hydration of Na+(H2O)n=1-7 Clusters: DFT Study
  26. A proposed image-based detection of methamidophos pesticide using peroxyoxalate chemiluminescence system
  27. Phytochemical screening and estrogenic activity of total glycosides of Cistanche deserticola
  28. Biological evaluation of a series of benzothiazole derivatives as mosquitocidal agents
  29. Chemical pretreatments of Trapa bispinosa's peel (TBP) biosorbent to enhance adsorption capacity for Pb(ll)
  30. Dynamic Changes in MMP1 and TIMP1 in the Antifibrotic Process of Dahuang Zhechong Pill in Rats with Liver Fibrosis
  31. The Optimization and Production of Ginkgolide B Lipid Microemulsion
  32. Photodynamic Therapy Enhanced the Antitumor Effects of Berberine on HeLa Cells
  33. Chiral and Achiral Enantiomeric Separation of (±)-Alprenolol
  34. Correlation of Water Fluoride with Body Fluids, Dental Fluorosis and FT4, FT3 –TSH Disruption among Children in an Endemic Fluorosis area in Pakistan
  35. A one-step incubation ELISA kit for rapid determination of dibutyl phthalate in water, beverage and liquor
  36. Free Radical Scavenging Activity of Essential Oil of Eugenia caryophylata from Amboina Island and Derivatives of Eugenol
  37. Effects of Blue and Red Light On Growth And Nitrate Metabolism In Pakchoi
  38. miRNA-199a-5p functions as a tumor suppressor in prolactinomas
  39. Solar photodegradation of carbamazepine from aqueous solutions using a compound parabolic concentrator equipped with a sun tracking system
  40. Influence of sub-inhibitory concentration of selected plant essential oils on the physical and biochemical properties of Pseudomonas orientalis
  41. Preparation and spectroscopic studies of Fe(II), Ru(II), Pd(II) and Zn(II) complexes of Schiff base containing terephthalaldehyde and their transfer hydrogenation and Suzuki-Miyaura coupling reaction
  42. Complex formation in a liquid-liquid extraction-chromogenic system for vanadium(IV)
  43. Synthesis, characterization (IR, 1H, 13C & 31P NMR), fungicidal, herbicidal and molecular docking evaluation of steroid phosphorus compounds
  44. Analysis and Biological Evaluation of Arisaema Amuremse Maxim Essential Oil
  45. A preliminary assessment of potential ecological risk and soil contamination by heavy metals around a cement factory, western Saudi Arabia
  46. Anti- inflammatory effect of Prunus tomentosa Thunb total flavones in LPS-induced RAW264.7 cells
  47. Collaborative Influence of Elevated CO2 Concentration and High Temperature on Potato Biomass Accumulation and Characteristics
  48. Methods of extraction, physicochemical properties of alginates and their applications in biomedical field – a review
  49. Characteristics of liposomes derived from egg yolk
  50. Preparation of ternary ZnO/Ag/cellulose and its enhanced photocatalytic degradation property on phenol and benzene in VOCs
  51. Influence of Human Serum Albumin Glycation on the Binding Affinities for Natural Flavonoids
  52. Synthesis and antioxidant activity of 2-methylthio-pyrido[3,2-e][1,2,4] triazolo[1,5-a]pyrimidines
  53. Comparative study on the antioxidant activities of ten common flower teas from China
  54. Molecular Properties of Symmetrical Networks Using Topological Polynomials
  55. Synthesis of Co3O4 Nano Aggregates by Co-precipitation Method and its Catalytic and Fuel Additive Applications
  56. Phytochemical analysis, Antioxidant and Antiprotoscolices potential of ethanol extracts of selected plants species against Echinococcus granulosus: In-vitro study
  57. Silver nanoparticles enhanced fluorescence for sensitive determination of fluoroquinolones in water solutions
  58. Simultaneous Quantification of the New Psychoactive Substances 3-FMC, 3-FPM, 4-CEC, and 4-BMC in Human Blood using GC-MS
  59. Biodiesel Production by Lipids From Indonesian strain of Microalgae Chlorella vulgaris
  60. Miscibility studies of polystyrene/polyvinyl chloride blend in presence of organoclay
  61. Antibacterial Activities of Transition Metal complexes of Mesocyclic Amidine 1,4-diazacycloheptane (DACH)
  62. Novel 1,8-Naphthyridine Derivatives: Design, Synthesis and in vitro screening of their cytotoxic activity against MCF7 cell line
  63. Investigation of Stress Corrosion Cracking Behaviour of Mg-Al-Zn Alloys in Different pH Environments by SSRT Method
  64. Various Combinations of Flame Retardants for Poly (vinyl chloride)
  65. Phenolic compounds and biological activities of rye (Secale cereale L.) grains
  66. Oxidative degradation of gentamicin present in water by an electro-Fenton process and biodegradability improvement
  67. Optimizing Suitable Conditions for the Removal of Ammonium Nitrogen by a Microbe Isolated from Chicken Manure
  68. Anti-inflammatory, antipyretic, analgesic, and antioxidant activities of Haloxylon salicornicum aqueous fraction
  69. The anti-corrosion behaviour of Satureja montana L. extract on iron in NaCl solution
  70. Interleukin-4, hemopexin, and lipoprotein-associated phospholipase A2 are significantly increased in patients with unstable carotid plaque
  71. A comparative study of the crystal structures of 2-(4-(2-(4-(3-chlorophenyl)pipera -zinyl)ethyl) benzyl)isoindoline-1,3-dione by synchrotron radiation X-ray powder diffraction and single-crystal X-ray diffraction
  72. Conceptual DFT as a Novel Chemoinformatics Tool for Studying the Chemical Reactivity Properties of the Amatoxin Family of Fungal Peptides
  73. Occurrence of Aflatoxin M1 in Milk-based Mithae samples from Pakistan
  74. Kinetics of Iron Removal From Ti-Extraction Blast Furnace Slag by Chlorination Calcination
  75. Increasing the activity of DNAzyme based on the telomeric sequence: 2’-OMe-RNA and LNA modifications
  76. Exploring the optoelectronic properties of a chromene-appended pyrimidone derivative for photovoltaic applications
  77. Effect of He Qi San on DNA Methylation in Type 2 Diabetes Mellitus Patients with Phlegm-blood Stasis Syndrome
  78. Cyclodextrin potentiometric sensors based on selective recognition sites for procainamide: Comparative and theoretical study
  79. Greener synthesis of dimethyl carbonate from carbon dioxide and methanol using a tunable ionic liquid catalyst
  80. Nonisothermal Cold Crystallization Kinetics of Poly(lactic acid)/Bacterial Poly(hydroxyoctanoate) (PHO)/Talc
  81. Enhanced adsorption of sulfonamide antibiotics in water by modified biochar derived from bagasse
  82. Study on the Mechanism of Shugan Xiaozhi Fang on Cells with Non-alcoholic Fatty Liver Disease
  83. Comparative Effects of Salt and Alkali Stress on Antioxidant System in Cotton (Gossypium Hirsutum L.) Leaves
  84. Optimization of chromatographic systems for analysis of selected psychotropic drugs and their metabolites in serum and saliva by HPLC in order to monitor therapeutic drugs
  85. Electrocatalytic Properties of Ni-Doped BaFe12O19 for Oxygen Evolution in Alkaline Solution
  86. Study on the removal of high contents of ammonium from piggery wastewater by clinoptilolite and the corresponding mechanisms
  87. Phytochemistry and toxicological assessment of Bryonia dioica roots used in north-African alternative medicine
  88. The essential oil composition of selected Hemerocallis cultivars and their biological activity
  89. Mechanical Properties of Carbon Fiber Reinforced Nanocrystalline Nickel Composite Electroforming Deposit
  90. Anti-c-myc efficacy block EGFL7 induced prolactinoma tumorigenesis
  91. Topical Issue on Applications of Mathematics in Chemistry
  92. Zagreb Connection Number Index of Nanotubes and Regular Hexagonal Lattice
  93. The Sanskruti index of trees and unicyclic graphs
  94. Valency-based molecular descriptors of Bakelite network BNmn
  95. Computing Topological Indices for Para-Line Graphs of Anthracene
  96. Zagreb Polynomials and redefined Zagreb indices of Dendrimers and Polyomino Chains
  97. Topological Descriptor of 2-Dimensional Silicon Carbons and Their Applications
  98. Topological invariants for the line graphs of some classes of graphs
  99. Words for maximal Subgroups of Fi24‘
  100. Generators of Maximal Subgroups of Harada-Norton and some Linear Groups
  101. Special Issue on POKOCHA 2018
  102. Influence of Production Parameters on the Content of Polyphenolic Compounds in Extruded Porridge Enriched with Chokeberry Fruit (Aronia melanocarpa (Michx.) Elliott)
  103. Effects of Supercritical Carbon Dioxide Extraction (SC-CO2) on the content of tiliroside in the extracts from Tilia L. flowers
  104. Impact of xanthan gum addition on phenolic acids composition and selected properties of new gluten-free maize-field bean pasta
  105. Impact of storage temperature and time on Moldavian dragonhead oil – spectroscopic and chemometric analysis
  106. The effect of selected substances on the stability of standard solutions in voltammetric analysis of ascorbic acid in fruit juices
  107. Determination of the content of Pb, Cd, Cu, Zn in dairy products from various regions of Poland
  108. Special Issue on IC3PE 2018 Conference
  109. The Photocatalytic Activity of Zns-TiO2 on a Carbon Fiber Prepared by Chemical Bath Deposition
  110. N-octyl chitosan derivatives as amphiphilic carrier agents for herbicide formulations
  111. Kinetics and Mechanistic Study of Hydrolysis of Adenosine Monophosphate Disodium Salt (AMPNa2) in Acidic and Alkaline Media
  112. Antimalarial Activity of Andrographis Paniculata Ness‘s N-hexane Extract and Its Major Compounds
  113. Special Issue on ABB2018 Conference
  114. Special Issue on ICCESEN 2017
  115. Theoretical Diagnostics of Second and Third-order Hyperpolarizabilities of Several Acid Derivatives
  116. Determination of Gamma Rays Efficiency Against Rhizoctonia solani in Potatoes
  117. Studies On Compatibilization Of Recycled Polyethylene/Thermoplastic Starch Blends By Using Different Compatibilizer
  118. Liquid−Liquid Extraction of Linalool from Methyl Eugenol with 1-Ethyl-3-methylimidazolium Hydrogen Sulfate [EMIM][HSO4] Ionic Liquid
  119. Synthesis of Graphene Oxide Through Ultrasonic Assisted Electrochemical Exfoliation
  120. Special Issue on ISCMP 2018
  121. Synthesis and antiproliferative evaluation of some 1,4-naphthoquinone derivatives against human cervical cancer cells
  122. The influence of the grafted aryl groups on the solvation properties of the graphyne and graphdiyne - a MD study
  123. Electrochemical modification of platinum and glassy carbon surfaces with pyridine layers and their use as complexing agents for copper (II) ions
  124. Effect of Electrospinning Process on Total Antioxidant Activity of Electrospun Nanofibers Containing Grape Seed Extract
  125. Effect Of Thermal Treatment Of Trepel At Temperature Range 800-1200˚C
  126. Topical Issue on Agriculture
  127. The effect of Cladophora glomerata exudates on the amino acid composition of Cladophora fracta and Rhizoclonium sp.
  128. Influence of the Static Magnetic Field and Algal Extract on the Germination of Soybean Seeds
  129. The use of UV-induced fluorescence for the assessment of homogeneity of granular mixtures
  130. The use of microorganisms as bio-fertilizers in the cultivation of white lupine
  131. Lyophilized apples on flax oil and ethyl esters of flax oil - stability and antioxidant evaluation
  132. Production of phosphorus biofertilizer based on the renewable materials in large laboratory scale
  133. Human health risk assessment of potential toxic elements in paddy soil and rice (Oryza sativa) from Ugbawka fields, Enugu, Nigeria
  134. Recovery of phosphates(V) from wastewaters of different chemical composition
  135. Special Issue on the 4th Green Chemistry 2018
  136. Dead zone for hydrogenation of propylene reaction carried out on commercial catalyst pellets
  137. Improved thermally stable oligoetherols from 6-aminouracil, ethylene carbonate and boric acid
  138. The role of a chemical loop in removal of hazardous contaminants from coke oven wastewater during its treatment
  139. Combating paraben pollution in surface waters with a variety of photocatalyzed systems: Looking for the most efficient technology
  140. Special Issue on Chemistry Today for Tomorrow 2019
  141. Applying Discriminant and Cluster Analyses to Separate Allergenic from Non-allergenic Proteins
  142. Chemometric Expertise Of Clinical Monitoring Data Of Prolactinoma Patients
  143. Chemomertic Risk Assessment of Soil Pollution
  144. New composite sorbent for speciation analysis of soluble chromium in textiles
  145. Photocatalytic activity of NiFe2O4 and Zn0.5Ni0.5Fe2O4 modified by Eu(III) and Tb(III) for decomposition of Malachite Green
  146. Photophysical and antibacterial activity of light-activated quaternary eosin Y
  147. Spectral properties and biological activity of La(III) and Nd(III) Monensinates
  148. Special Issue on Monitoring, Risk Assessment and Sustainable Management for the Exposure to Environmental Toxins
  149. Soil organic carbon mineralization in relation to microbial dynamics in subtropical red soils dominated by differently sized aggregates
  150. A potential reusable fluorescent aptasensor based on magnetic nanoparticles for ochratoxin A analysis
  151. Special Issue on 13th JCC 2018
  152. Fluorescence study of 5-nitroisatin Schiff base immobilized on SBA-15 for sensing Fe3+
  153. Thermal and Morphology Properties of Cellulose Nanofiber from TEMPO-oxidized Lower part of Empty Fruit Bunches (LEFB)
  154. Encapsulation of Vitamin C in Sesame Liposomes: Computational and Experimental Studies
  155. A comparative study of the utilization of synthetic foaming agent and aluminum powder as pore-forming agents in lightweight geopolymer synthesis
  156. Synthesis of high surface area mesoporous silica SBA-15 by adjusting hydrothermal treatment time and the amount of polyvinyl alcohol
  157. Review of large-pore mesostructured cellular foam (MCF) silica and its applications
  158. Ion Exchange of Benzoate in Ni-Al-Benzoate Layered Double Hydroxide by Amoxicillin
  159. Synthesis And Characterization Of CoMo/Mordenite Catalyst For Hydrotreatment Of Lignin Compound Models
  160. Production of Biodiesel from Nyamplung (Calophyllum inophyllum L.) using Microwave with CaO Catalyst from Eggshell Waste: Optimization of Transesterification Process Parameters
  161. The Study of the Optical Properties of C60 Fullerene in Different Organic Solvents
  162. Composite Material Consisting of HKUST-1 and Indonesian Activated Natural Zeolite and its Application in CO2 Capture
  163. Topical Issue on Environmental Chemistry
  164. Ionic liquids modified cobalt/ZSM-5 as a highly efficient catalyst for enhancing the selectivity towards KA oil in the aerobic oxidation of cyclohexane
  165. Application of Thermal Resistant Gemini Surfactants in Highly Thixotropic Water-in-oil Drilling Fluid System
  166. Screening Study on Rheological Behavior and Phase Transition Point of Polymer-containing Fluids produced under the Oil Freezing Point Temperature
  167. The Chemical Softening Effect and Mechanism of Low Rank Coal Soaked in Alkaline Solution
  168. The Influence Of NO/O2 On The NOx Storage Properties Over A Pt-Ba-Ce/γ-Al2O3 Catalyst
  169. Special Issue on the International conference CosCI 2018
  170. Design of SiO2/TiO2 that Synergistically Increases The Hydrophobicity of Methyltrimethoxysilane Coated Glass
  171. Antidiabetes and Antioxidant agents from Clausena excavata root as medicinal plant of Myanmar
  172. Development of a Gold Immunochromatographic Assay Method Using Candida Biofilm Antigen as a Bioreceptor for Candidiasis in Rats
  173. Special Issue on Applied Biochemistry and Biotechnology 2019
  174. Adsorption of copper ions on Magnolia officinalis residues after solid-phase fermentation with Phanerochaete chrysosporium
  175. Erratum
  176. Erratum to: Sand Dune Characterization For Preparing Metallurgical Grade Silicon
https://doi.org/10.1515/chem-2019-0144
Keywords for this article
Zagreb Index; Zagreb Polynomial; Dendrimers; Polyomino chain; Chemical graph theory
Creative Commons
BY 4.0

Articles in the same Issue

  1. Regular Articles
  2. Research on correlation of compositions with oestrogenic activity of Cistanche based on LC/Q-TOF-MS/MS technology
  3. Efficacy of Pyrus elaeagnifolia subsp. elaeagnifolia in acetic acid–induced colitis model
  4. Anti-inflammatory and antinociceptive features of Bryonia alba L.: As a possible alternative in treating rheumatism
  5. High efficiency liposome fusion induced by reducing undesired membrane peptides interaction
  6. Prediction of the Blood-Brain Barrier Permeability Using RP-18 Thin Layer Chromatography
  7. Phytic Acid Extracted from Rice Bran as a Growth Promoter for Euglena gracilis
  8. Development of a validated spectrofluorimetric method for assay of sotalol hydrochloride in tablets and human plasma: application for stability-indicating studies
  9. Topological Indices of Hyaluronic Acid-Paclitaxel Conjugates’ Molecular Structure in Cancer Treatment
  10. Thermodynamic properties of the bubble growth process in a pool boiling of water-ethanol mixture two-component system
  11. Critical Roles of the PI3K-Akt-mTOR Signaling Pathway in Apoptosis and Autophagy of Astrocytes Induced by Methamphetamine
  12. Characteristics of Stable Hydrogen and Oxygen Isotopes of Soil Moisture under Different Land Use in Dry Hot Valley of Yuanmou
  13. Specific, highly sensitive and simple spectrofluorimetric method for quantification of daclatasvir in HCV human plasma patients and in tablets dosage form
  14. Chromium-modified cobalt molybdenum nitrides as catalysts for ammonia synthesis
  15. Langerhans cell-like dendritic cells treated with ginsenoside Rh2 regulate the differentiation of Th1 and Th2 cells in vivo
  16. Identification of Powdery Mildew Blumeria graminis f. sp. tritici Resistance Genes in Selected Wheat Varieties and Development of Multiplex PCR
  17. Computational Analysis of new Degree-based descriptors of oxide networks
  18. The Use Of Chemical Composition And Additives To Classify Petrol And Diesel Using Gas Chromatography–Mass Spectrometry And Chemometric Analysis: A Uk Study
  19. Minimal Energy Tree with 4 Branched Vertices
  20. Jatropha seed oil derived poly(esteramide-urethane)/ fumed silica nanocomposite coatings for corrosion protection
  21. Calculating topological indices of certain OTIS interconnection networks
  22. Energy storage analysis of R125 in UIO-66 and MOF-5 nanoparticles: A molecular simulation study
  23. Velvet Antler compounds targeting major cell signaling pathways in osteosarcoma - a new insight into mediating the process of invasion and metastasis in OS
  24. Effects of Azadirachta Indica Leaf Extract, Capping Agents, on the Synthesis of Pure And Cu Doped ZnO-Nanoparticles: A Green Approach and Microbial Activity
  25. Aqueous Micro-hydration of Na+(H2O)n=1-7 Clusters: DFT Study
  26. A proposed image-based detection of methamidophos pesticide using peroxyoxalate chemiluminescence system
  27. Phytochemical screening and estrogenic activity of total glycosides of Cistanche deserticola
  28. Biological evaluation of a series of benzothiazole derivatives as mosquitocidal agents
  29. Chemical pretreatments of Trapa bispinosa's peel (TBP) biosorbent to enhance adsorption capacity for Pb(ll)
  30. Dynamic Changes in MMP1 and TIMP1 in the Antifibrotic Process of Dahuang Zhechong Pill in Rats with Liver Fibrosis
  31. The Optimization and Production of Ginkgolide B Lipid Microemulsion
  32. Photodynamic Therapy Enhanced the Antitumor Effects of Berberine on HeLa Cells
  33. Chiral and Achiral Enantiomeric Separation of (±)-Alprenolol
  34. Correlation of Water Fluoride with Body Fluids, Dental Fluorosis and FT4, FT3 –TSH Disruption among Children in an Endemic Fluorosis area in Pakistan
  35. A one-step incubation ELISA kit for rapid determination of dibutyl phthalate in water, beverage and liquor
  36. Free Radical Scavenging Activity of Essential Oil of Eugenia caryophylata from Amboina Island and Derivatives of Eugenol
  37. Effects of Blue and Red Light On Growth And Nitrate Metabolism In Pakchoi
  38. miRNA-199a-5p functions as a tumor suppressor in prolactinomas
  39. Solar photodegradation of carbamazepine from aqueous solutions using a compound parabolic concentrator equipped with a sun tracking system
  40. Influence of sub-inhibitory concentration of selected plant essential oils on the physical and biochemical properties of Pseudomonas orientalis
  41. Preparation and spectroscopic studies of Fe(II), Ru(II), Pd(II) and Zn(II) complexes of Schiff base containing terephthalaldehyde and their transfer hydrogenation and Suzuki-Miyaura coupling reaction
  42. Complex formation in a liquid-liquid extraction-chromogenic system for vanadium(IV)
  43. Synthesis, characterization (IR, 1H, 13C & 31P NMR), fungicidal, herbicidal and molecular docking evaluation of steroid phosphorus compounds
  44. Analysis and Biological Evaluation of Arisaema Amuremse Maxim Essential Oil
  45. A preliminary assessment of potential ecological risk and soil contamination by heavy metals around a cement factory, western Saudi Arabia
  46. Anti- inflammatory effect of Prunus tomentosa Thunb total flavones in LPS-induced RAW264.7 cells
  47. Collaborative Influence of Elevated CO2 Concentration and High Temperature on Potato Biomass Accumulation and Characteristics
  48. Methods of extraction, physicochemical properties of alginates and their applications in biomedical field – a review
  49. Characteristics of liposomes derived from egg yolk
  50. Preparation of ternary ZnO/Ag/cellulose and its enhanced photocatalytic degradation property on phenol and benzene in VOCs
  51. Influence of Human Serum Albumin Glycation on the Binding Affinities for Natural Flavonoids
  52. Synthesis and antioxidant activity of 2-methylthio-pyrido[3,2-e][1,2,4] triazolo[1,5-a]pyrimidines
  53. Comparative study on the antioxidant activities of ten common flower teas from China
  54. Molecular Properties of Symmetrical Networks Using Topological Polynomials
  55. Synthesis of Co3O4 Nano Aggregates by Co-precipitation Method and its Catalytic and Fuel Additive Applications
  56. Phytochemical analysis, Antioxidant and Antiprotoscolices potential of ethanol extracts of selected plants species against Echinococcus granulosus: In-vitro study
  57. Silver nanoparticles enhanced fluorescence for sensitive determination of fluoroquinolones in water solutions
  58. Simultaneous Quantification of the New Psychoactive Substances 3-FMC, 3-FPM, 4-CEC, and 4-BMC in Human Blood using GC-MS
  59. Biodiesel Production by Lipids From Indonesian strain of Microalgae Chlorella vulgaris
  60. Miscibility studies of polystyrene/polyvinyl chloride blend in presence of organoclay
  61. Antibacterial Activities of Transition Metal complexes of Mesocyclic Amidine 1,4-diazacycloheptane (DACH)
  62. Novel 1,8-Naphthyridine Derivatives: Design, Synthesis and in vitro screening of their cytotoxic activity against MCF7 cell line
  63. Investigation of Stress Corrosion Cracking Behaviour of Mg-Al-Zn Alloys in Different pH Environments by SSRT Method
  64. Various Combinations of Flame Retardants for Poly (vinyl chloride)
  65. Phenolic compounds and biological activities of rye (Secale cereale L.) grains
  66. Oxidative degradation of gentamicin present in water by an electro-Fenton process and biodegradability improvement
  67. Optimizing Suitable Conditions for the Removal of Ammonium Nitrogen by a Microbe Isolated from Chicken Manure
  68. Anti-inflammatory, antipyretic, analgesic, and antioxidant activities of Haloxylon salicornicum aqueous fraction
  69. The anti-corrosion behaviour of Satureja montana L. extract on iron in NaCl solution
  70. Interleukin-4, hemopexin, and lipoprotein-associated phospholipase A2 are significantly increased in patients with unstable carotid plaque
  71. A comparative study of the crystal structures of 2-(4-(2-(4-(3-chlorophenyl)pipera -zinyl)ethyl) benzyl)isoindoline-1,3-dione by synchrotron radiation X-ray powder diffraction and single-crystal X-ray diffraction
  72. Conceptual DFT as a Novel Chemoinformatics Tool for Studying the Chemical Reactivity Properties of the Amatoxin Family of Fungal Peptides
  73. Occurrence of Aflatoxin M1 in Milk-based Mithae samples from Pakistan
  74. Kinetics of Iron Removal From Ti-Extraction Blast Furnace Slag by Chlorination Calcination
  75. Increasing the activity of DNAzyme based on the telomeric sequence: 2’-OMe-RNA and LNA modifications
  76. Exploring the optoelectronic properties of a chromene-appended pyrimidone derivative for photovoltaic applications
  77. Effect of He Qi San on DNA Methylation in Type 2 Diabetes Mellitus Patients with Phlegm-blood Stasis Syndrome
  78. Cyclodextrin potentiometric sensors based on selective recognition sites for procainamide: Comparative and theoretical study
  79. Greener synthesis of dimethyl carbonate from carbon dioxide and methanol using a tunable ionic liquid catalyst
  80. Nonisothermal Cold Crystallization Kinetics of Poly(lactic acid)/Bacterial Poly(hydroxyoctanoate) (PHO)/Talc
  81. Enhanced adsorption of sulfonamide antibiotics in water by modified biochar derived from bagasse
  82. Study on the Mechanism of Shugan Xiaozhi Fang on Cells with Non-alcoholic Fatty Liver Disease
  83. Comparative Effects of Salt and Alkali Stress on Antioxidant System in Cotton (Gossypium Hirsutum L.) Leaves
  84. Optimization of chromatographic systems for analysis of selected psychotropic drugs and their metabolites in serum and saliva by HPLC in order to monitor therapeutic drugs
  85. Electrocatalytic Properties of Ni-Doped BaFe12O19 for Oxygen Evolution in Alkaline Solution
  86. Study on the removal of high contents of ammonium from piggery wastewater by clinoptilolite and the corresponding mechanisms
  87. Phytochemistry and toxicological assessment of Bryonia dioica roots used in north-African alternative medicine
  88. The essential oil composition of selected Hemerocallis cultivars and their biological activity
  89. Mechanical Properties of Carbon Fiber Reinforced Nanocrystalline Nickel Composite Electroforming Deposit
  90. Anti-c-myc efficacy block EGFL7 induced prolactinoma tumorigenesis
  91. Topical Issue on Applications of Mathematics in Chemistry
  92. Zagreb Connection Number Index of Nanotubes and Regular Hexagonal Lattice
  93. The Sanskruti index of trees and unicyclic graphs
  94. Valency-based molecular descriptors of Bakelite network BNmn
  95. Computing Topological Indices for Para-Line Graphs of Anthracene
  96. Zagreb Polynomials and redefined Zagreb indices of Dendrimers and Polyomino Chains
  97. Topological Descriptor of 2-Dimensional Silicon Carbons and Their Applications
  98. Topological invariants for the line graphs of some classes of graphs
  99. Words for maximal Subgroups of Fi24‘
  100. Generators of Maximal Subgroups of Harada-Norton and some Linear Groups
  101. Special Issue on POKOCHA 2018
  102. Influence of Production Parameters on the Content of Polyphenolic Compounds in Extruded Porridge Enriched with Chokeberry Fruit (Aronia melanocarpa (Michx.) Elliott)
  103. Effects of Supercritical Carbon Dioxide Extraction (SC-CO2) on the content of tiliroside in the extracts from Tilia L. flowers
  104. Impact of xanthan gum addition on phenolic acids composition and selected properties of new gluten-free maize-field bean pasta
  105. Impact of storage temperature and time on Moldavian dragonhead oil – spectroscopic and chemometric analysis
  106. The effect of selected substances on the stability of standard solutions in voltammetric analysis of ascorbic acid in fruit juices
  107. Determination of the content of Pb, Cd, Cu, Zn in dairy products from various regions of Poland
  108. Special Issue on IC3PE 2018 Conference
  109. The Photocatalytic Activity of Zns-TiO2 on a Carbon Fiber Prepared by Chemical Bath Deposition
  110. N-octyl chitosan derivatives as amphiphilic carrier agents for herbicide formulations
  111. Kinetics and Mechanistic Study of Hydrolysis of Adenosine Monophosphate Disodium Salt (AMPNa2) in Acidic and Alkaline Media
  112. Antimalarial Activity of Andrographis Paniculata Ness‘s N-hexane Extract and Its Major Compounds
  113. Special Issue on ABB2018 Conference
  114. Special Issue on ICCESEN 2017
  115. Theoretical Diagnostics of Second and Third-order Hyperpolarizabilities of Several Acid Derivatives
  116. Determination of Gamma Rays Efficiency Against Rhizoctonia solani in Potatoes
  117. Studies On Compatibilization Of Recycled Polyethylene/Thermoplastic Starch Blends By Using Different Compatibilizer
  118. Liquid−Liquid Extraction of Linalool from Methyl Eugenol with 1-Ethyl-3-methylimidazolium Hydrogen Sulfate [EMIM][HSO4] Ionic Liquid
  119. Synthesis of Graphene Oxide Through Ultrasonic Assisted Electrochemical Exfoliation
  120. Special Issue on ISCMP 2018
  121. Synthesis and antiproliferative evaluation of some 1,4-naphthoquinone derivatives against human cervical cancer cells
  122. The influence of the grafted aryl groups on the solvation properties of the graphyne and graphdiyne - a MD study
  123. Electrochemical modification of platinum and glassy carbon surfaces with pyridine layers and their use as complexing agents for copper (II) ions
  124. Effect of Electrospinning Process on Total Antioxidant Activity of Electrospun Nanofibers Containing Grape Seed Extract
  125. Effect Of Thermal Treatment Of Trepel At Temperature Range 800-1200˚C
  126. Topical Issue on Agriculture
  127. The effect of Cladophora glomerata exudates on the amino acid composition of Cladophora fracta and Rhizoclonium sp.
  128. Influence of the Static Magnetic Field and Algal Extract on the Germination of Soybean Seeds
  129. The use of UV-induced fluorescence for the assessment of homogeneity of granular mixtures
  130. The use of microorganisms as bio-fertilizers in the cultivation of white lupine
  131. Lyophilized apples on flax oil and ethyl esters of flax oil - stability and antioxidant evaluation
  132. Production of phosphorus biofertilizer based on the renewable materials in large laboratory scale
  133. Human health risk assessment of potential toxic elements in paddy soil and rice (Oryza sativa) from Ugbawka fields, Enugu, Nigeria
  134. Recovery of phosphates(V) from wastewaters of different chemical composition
  135. Special Issue on the 4th Green Chemistry 2018
  136. Dead zone for hydrogenation of propylene reaction carried out on commercial catalyst pellets
  137. Improved thermally stable oligoetherols from 6-aminouracil, ethylene carbonate and boric acid
  138. The role of a chemical loop in removal of hazardous contaminants from coke oven wastewater during its treatment
  139. Combating paraben pollution in surface waters with a variety of photocatalyzed systems: Looking for the most efficient technology
  140. Special Issue on Chemistry Today for Tomorrow 2019
  141. Applying Discriminant and Cluster Analyses to Separate Allergenic from Non-allergenic Proteins
  142. Chemometric Expertise Of Clinical Monitoring Data Of Prolactinoma Patients
  143. Chemomertic Risk Assessment of Soil Pollution
  144. New composite sorbent for speciation analysis of soluble chromium in textiles
  145. Photocatalytic activity of NiFe2O4 and Zn0.5Ni0.5Fe2O4 modified by Eu(III) and Tb(III) for decomposition of Malachite Green
  146. Photophysical and antibacterial activity of light-activated quaternary eosin Y
  147. Spectral properties and biological activity of La(III) and Nd(III) Monensinates
  148. Special Issue on Monitoring, Risk Assessment and Sustainable Management for the Exposure to Environmental Toxins
  149. Soil organic carbon mineralization in relation to microbial dynamics in subtropical red soils dominated by differently sized aggregates
  150. A potential reusable fluorescent aptasensor based on magnetic nanoparticles for ochratoxin A analysis
  151. Special Issue on 13th JCC 2018
  152. Fluorescence study of 5-nitroisatin Schiff base immobilized on SBA-15 for sensing Fe3+
  153. Thermal and Morphology Properties of Cellulose Nanofiber from TEMPO-oxidized Lower part of Empty Fruit Bunches (LEFB)
  154. Encapsulation of Vitamin C in Sesame Liposomes: Computational and Experimental Studies
  155. A comparative study of the utilization of synthetic foaming agent and aluminum powder as pore-forming agents in lightweight geopolymer synthesis
  156. Synthesis of high surface area mesoporous silica SBA-15 by adjusting hydrothermal treatment time and the amount of polyvinyl alcohol
  157. Review of large-pore mesostructured cellular foam (MCF) silica and its applications
  158. Ion Exchange of Benzoate in Ni-Al-Benzoate Layered Double Hydroxide by Amoxicillin
  159. Synthesis And Characterization Of CoMo/Mordenite Catalyst For Hydrotreatment Of Lignin Compound Models
  160. Production of Biodiesel from Nyamplung (Calophyllum inophyllum L.) using Microwave with CaO Catalyst from Eggshell Waste: Optimization of Transesterification Process Parameters
  161. The Study of the Optical Properties of C60 Fullerene in Different Organic Solvents
  162. Composite Material Consisting of HKUST-1 and Indonesian Activated Natural Zeolite and its Application in CO2 Capture
  163. Topical Issue on Environmental Chemistry
  164. Ionic liquids modified cobalt/ZSM-5 as a highly efficient catalyst for enhancing the selectivity towards KA oil in the aerobic oxidation of cyclohexane
  165. Application of Thermal Resistant Gemini Surfactants in Highly Thixotropic Water-in-oil Drilling Fluid System
  166. Screening Study on Rheological Behavior and Phase Transition Point of Polymer-containing Fluids produced under the Oil Freezing Point Temperature
  167. The Chemical Softening Effect and Mechanism of Low Rank Coal Soaked in Alkaline Solution
  168. The Influence Of NO/O2 On The NOx Storage Properties Over A Pt-Ba-Ce/γ-Al2O3 Catalyst
  169. Special Issue on the International conference CosCI 2018
  170. Design of SiO2/TiO2 that Synergistically Increases The Hydrophobicity of Methyltrimethoxysilane Coated Glass
  171. Antidiabetes and Antioxidant agents from Clausena excavata root as medicinal plant of Myanmar
  172. Development of a Gold Immunochromatographic Assay Method Using Candida Biofilm Antigen as a Bioreceptor for Candidiasis in Rats
  173. Special Issue on Applied Biochemistry and Biotechnology 2019
  174. Adsorption of copper ions on Magnolia officinalis residues after solid-phase fermentation with Phanerochaete chrysosporium
  175. Erratum
  176. Erratum to: Sand Dune Characterization For Preparing Metallurgical Grade Silicon
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 5.10.2025 from https://www.degruyterbrill.com/document/doi/10.1515/chem-2019-0144/html
Scroll to top button