Abstract
In recent years, several structure-based properties of the molecular graphs are understood through the chemical graph theory. The molecular graph
1 Introduction
The chemical, physical, and physicochemical properties of a compound, which depends on its structure, can be effectively studied by means of the graph theory. A chemical structure of a compound can be described by a graph
Before proceeding further regarding the definitions of the topological indices studied in this paper, we recall the relevant notions and set the corresponding notations. For the notions and notations not described here we refer [12] to the readers. Throughout this paper, we denote a simple connected graph by
According to the settings described in the previous paragraph, the first K-Banhatti index
The modified first K-Banhatti index
The first K-hyper Banhatti index
The first- and second-hyper Revan indices of
where
On the other hand, silicon is a nontoxic semiconductor material that has a very low cost when compared with other materials of the same type. Silicon is a vital part of all electronic devices. The well-constructed structures of two-dimensional (2D) silicon–carbon single layer compounds having different stoichiometric compositions were concluded in ref. [17]. The 2D silicon–carbon single layer may be seen as configurable materials between the pure 2D carbon single layer, graphene, and the pure 2D silicon single layer, silicene. After many attempts, the structure of the SiC sheet (with remarkable stability) was predicted, and for further details about this structure, we refer [18,19,20] to the readers. We consider 2D SiC compounds with a different types of silicon carbide structure-based on low-energy metastable structures for each silicon, that is,
By keeping in view the importance of the topological indices in theoretical and computational nano-sciences, we compute
2 Materials and methods
In Figure 1, the structure of silicon carbide
![Figure 1
(a) Unit cell of
Si
2
C
3
{{\rm{Si}}}_{2}{{\rm{C}}}_{3}
-
III
[
n
,
m
]
{\rm{III}}\left[n,m]
, (b)
Si
2
C
3
{{\rm{Si}}}_{2}{{\rm{C}}}_{3}
-III[5,4].](/document/doi/10.1515/chem-2020-0151/asset/graphic/j_chem-2020-0151_fig_001.jpg)
(a) Unit cell of
![Figure 2
(a) 2D structure of
Si
2
C
3
{{\rm{Si}}}_{2}{{\rm{C}}}_{3}
-III[5,1], (b) 2D structure of
Si
2
C
3
{{\rm{Si}}}_{2}{{\rm{C}}}_{3}
-III[5,2].](/document/doi/10.1515/chem-2020-0151/asset/graphic/j_chem-2020-0151_fig_002.jpg)
(a) 2D structure of
To compute the topological indices, we defined the partitions of vertices and edges of
Degree-based partition of edges of
|
Number of edges |
|
---|---|---|
(1, 3) | 2 | 2 |
(2, 2) |
|
2 |
(2, 3) |
|
3 |
(3, 3) |
|
4 |
To establish our results, we adopt an approach for combinatorial enrolling, an edge allocate, a vertex portion strategy, enlist hypothetical instruments, and degree counting procedure for vertices and edges. Moreover, we use Matlab and Maple for the estimations, attestation and plotting the obtained results. For further details, see refs. [8,24,25, 26,27].
3 Main results
In this section, we computed the formulas for the first and second K-Banhatti, modified K-Banhatti, K-hyper Banhatti, and hyper Revan indices of silicon carbide
Theorem 1
Let
Proof
Let
Second K-Banhatti index of
Theorem 2
Let
Proof
Let
Moreover, from the definition
Theorem 3
Let
Proof
Let
Second K-hyper Banhatti index of
Table 2 shows partition of edges of
Edge partition of
|
Number of edges |
|
|
---|---|---|---|
|
2 | 3 | 1 |
|
|
2 | 2 |
|
|
2 | 1 |
|
|
1 | 1 |
Theorem 4
Let
Proof
Let
Moreover, from the definition of
4 Graphical analysis
In Figure 3, K-Banhatti

Comparison of K-Banhatti
In Figure 4, modified K-Banhatti

Comparison of modified K-Banhatti
In Figure 5, K-hyper Banhatti

Comparison of K-hyper Banhatti
Figure 6 represents K-Banhatti

Comparison of first K-Banhatties indices.

Comparison of second K-Banhatties indices.
5 Discussion
In reticular chemistry, it is very difficult to investigate the physico-chemical properties and characterization of large chemical structures. However, topological indices are very useful in order to study such properties of large networks. The structural characteristics of the molecules are numerically represented by using the topological indices which may be obtained by applying the theoretical concept on these large networks. In this article, we gave precise formulas of some well-known topological indices for silicon carbide. In Figures 3–5, we have compared K-Banhatti
6 Conclusion and future work
Topological indices are helpful in predicting seeveral physico-chemical properties of the chemical compound. The applications of silicon carbide
Acknowledgment
The authors are thankful to the anonymous reviewers for their valuable comments, remarks, and suggestions to improve the quality of the paper.
-
Funding information: This research was conducted for the fulfillment of job requirement, no external funding was available for this research.
-
Author contributions: D.Z. – writing, review & editing; M.A.Z. – validation; R.I. – conceptualization, supervision; M.A. – writing, original draft, validation; A.F. – formal analysis, resources; Z.A. – methodology; L.L. – writing, review & editing.
-
Conflict of interest: Authors state no conflict of interest.
-
Ethical approval: The conducted research is not related to either human or animal use.
-
Data availability statement: Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
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© 2021 Dongming Zhao et al., published by De Gruyter
This work is licensed under the Creative Commons Attribution 4.0 International License.
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- Optimized extraction of polyphenols from leaves of Rosemary (Rosmarinus officinalis L.) grown in Lam Dong province, Vietnam, and evaluation of their antioxidant capacity
- Synthesis of novel thiourea-/urea-benzimidazole derivatives as anticancer agents
- Potency and selectivity indices of Myristica fragrans Houtt. mace chloroform extract against non-clinical and clinical human pathogens
- Simple modifications of nicotinic, isonicotinic, and 2,6-dichloroisonicotinic acids toward new weapons against plant diseases
- Synthesis, optical and structural characterisation of ZnS nanoparticles derived from Zn(ii) dithiocarbamate complexes
- Presence of short and cyclic peptides in Acacia and Ziziphus honeys may potentiate their medicinal values
- The role of vitamin D deficiency and elevated inflammatory biomarkers as risk factors for the progression of diabetic nephropathy in patients with type 2 diabetes mellitus
- Quantitative structure–activity relationship study on prolonged anticonvulsant activity of terpene derivatives in pentylenetetrazole test
- GADD45B induced the enhancing of cell viability and proliferation in radiotherapy and increased the radioresistance of HONE1 cells
- Cannabis sativa L. chemical compositions as potential plasmodium falciparum dihydrofolate reductase-thymidinesynthase enzyme inhibitors: An in silico study for drug development
- Dynamics of λ-cyhalothrin disappearance and expression of selected P450 genes in bees depending on the ambient temperature
- Identification of synthetic cannabinoid methyl 2-{[1-(cyclohexylmethyl)-1H-indol-3-yl] formamido}-3-methylbutanoate using modern mass spectrometry and nuclear magnetic resonance techniques
- Study on the speciation of arsenic in the genuine medicinal material honeysuckle
- Two Cu(ii)-based coordination polymers: Crystal structures and treatment activity on periodontitis
- Conversion of furfuryl alcohol to ethyl levulinate in the presence of mesoporous aluminosilicate catalyst
- Review Articles
- Hsien Wu and his major contributions to the chemical era of immunology
- Overview of the major classes of new psychoactive substances, psychoactive effects, analytical determination and conformational analysis of selected illegal drugs
- An overview of persistent organic pollutants along the coastal environment of Kuwait
- Mechanism underlying sevoflurane-induced protection in cerebral ischemia–reperfusion injury
- COVID-19 and SARS-CoV-2: Everything we know so far – A comprehensive review
- Challenge of diabetes mellitus and researchers’ contributions to its control
- Advances in the design and application of transition metal oxide-based supercapacitors
- Color and composition of beauty products formulated with lemongrass essential oil: Cosmetics formulation with lemongrass essential oil
- The structural chemistry of zinc(ii) and nickel(ii) dithiocarbamate complexes
- Bioprospecting for antituberculosis natural products – A review
- Recent progress in direct urea fuel cell
- Rapid Communications
- A comparative morphological study of titanium dioxide surface layer dental implants
- Changes in the antioxidative properties of honeys during their fermentation
- Erratum
- Erratum to “Corrosion study of copper in aqueous sulfuric acid solution in the presence of (2E,5E)-2,5-dibenzylidenecyclopentanone and (2E,5E)-bis[(4-dimethylamino)benzylidene]cyclopentanone: Experimental and theoretical study”
- Erratum to “Modified TDAE petroleum plasticiser”
- Corrigendum
- Corrigendum to “A nitric oxide-releasing prodrug promotes apoptosis in human renal carcinoma cells: Involvement of reactive oxygen species”
- Special Issue on 3rd IC3PE 2020
- Visible light-responsive photocatalyst of SnO2/rGO prepared using Pometia pinnata leaf extract
- Antihyperglycemic activity of Centella asiatica (L.) Urb. leaf ethanol extract SNEDDS in zebrafish (Danio rerio)
- Selection of oil extraction process from Chlorella species of microalgae by using multi-criteria decision analysis technique for biodiesel production
- Special Issue on the 14th Joint Conference of Chemistry (14JCC)
- Synthesis and in vitro cytotoxicity evaluation of isatin-pyrrole derivatives against HepG2 cell line
- CO2 gas separation using mixed matrix membranes based on polyethersulfone/MIL-100(Al)
- Effect of synthesis and activation methods on the character of CoMo/ultrastable Y-zeolite catalysts
- Special Issue on Electrochemical Amplified Sensors
- Enhancement of graphene oxide through β-cyclodextrin composite to sensitive analysis of an antidepressant: Sulpiride
- Investigation of the spectroelectrochemical behavior of quercetin isolated from Zanthoxylum bungeanum
- An electrochemical sensor for high sensitive determination of lysozyme based on the aptamer competition approach
- An improved non-enzymatic electrochemical sensor amplified with CuO nanostructures for sensitive determination of uric acid
- Special Issue on Applied Biochemistry and Biotechnology 2020
- Fast discrimination of avocado oil for different extracted methods using headspace-gas chromatography-ion mobility spectroscopy with PCA based on volatile organic compounds
- Effect of alkali bases on the synthesis of ZnO quantum dots
- Quality evaluation of Cabernet Sauvignon wines in different vintages by 1H nuclear magnetic resonance-based metabolomics
- Special Issue on the Joint Science Congress of Materials and Polymers (ISCMP 2019)
- Diatomaceous Earth: Characterization, thermal modification, and application
- Electrochemical determination of atenolol and propranolol using a carbon paste sensor modified with natural ilmenite
- Special Issue on the Conference of Energy, Fuels, Environment 2020
- Assessment of the mercury contamination of landfilled and recovered foundry waste – a case study
- Primary energy consumption in selected EU Countries compared to global trends
- Modified TDAE petroleum plasticiser
- Use of glycerol waste in lactic acid bacteria metabolism for the production of lactic acid: State of the art in Poland
- Topical Issue on Applications of Mathematics in Chemistry
- Theoretical study of energy, inertia and nullity of phenylene and anthracene
- Banhatti, revan and hyper-indices of silicon carbide Si2C3-III[n,m]
- Topical Issue on Agriculture
- Occurrence of mycotoxins in selected agricultural and commercial products available in eastern Poland
- Special Issue on Ethnobotanical, Phytochemical and Biological Investigation of Medicinal Plants
- Acute and repeated dose 60-day oral toxicity assessment of chemically characterized Berberis hispanica Boiss. and Reut in Wistar rats
- Phytochemical profile, in vitro antioxidant, and anti-protein denaturation activities of Curcuma longa L. rhizome and leaves
- Antiplasmodial potential of Eucalyptus obliqua leaf methanolic extract against Plasmodium vivax: An in vitro study
- Prunus padus L. bark as a functional promoting component in functional herbal infusions – cyclooxygenase-2 inhibitory, antioxidant, and antimicrobial effects
- Molecular and docking studies of tetramethoxy hydroxyflavone compound from Artemisia absinthium against carcinogens found in cigarette smoke
- Special Issue on the Joint Science Congress of Materials and Polymers (ISCMP 2020)
- Preparation of cypress (Cupressus sempervirens L.) essential oil loaded poly(lactic acid) nanofibers
- Influence of mica mineral on flame retardancy and mechanical properties of intumescent flame retardant polypropylene composites
- Production and characterization of thermoplastic elastomer foams based on the styrene–ethylene–butylene–styrene (SEBS) rubber and thermoplastic material
- Special Issue on Applied Chemistry in Agriculture and Food Science
- Impact of essential oils on the development of pathogens of the Fusarium genus and germination parameters of selected crops
- Yield, volume, quality, and reduction of biotic stress influenced by titanium application in oilseed rape, winter wheat, and maize cultivations
- Influence of potato variety on polyphenol profile composition and glycoalcaloid contents of potato juice
- Carryover effect of direct-fed microbial supplementation and early weaning on the growth performance and carcass characteristics of growing Najdi lambs
- Special Issue on Applied Biochemistry and Biotechnology (ABB 2021)
- The electrochemical redox mechanism and antioxidant activity of polyphenolic compounds based on inlaid multi-walled carbon nanotubes-modified graphite electrode
- Study of an adsorption method for trace mercury based on Bacillus subtilis
- Special Issue on The 1st Malaysia International Conference on Nanotechnology & Catalysis (MICNC2021)
- Mitigating membrane biofouling in biofuel cell system – A review
- Mechanical properties of polymeric biomaterials: Modified ePTFE using gamma irradiation