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On Topological Indices of Certain Dendrimer Structures

  • Adnan Aslam EMAIL logo , Yasir Bashir , Safyan Ahmad and Wei Gao
Published/Copyright: May 22, 2017

Abstract

A topological index can be considered as transformation of chemical structure in to real number. In QSAR/QSPR study, physicochemical properties and topological indices such as Randić, Zagreb, atom-bond connectivity ABC, and geometric-arithmetic GA index are used to predict the bioactivity of chemical compounds. Dendrimers are highly branched, star-shaped macromolecules with nanometer-scale dimensions. Dendrimers are defined by three components: a central core, an interior dendritic structure (the branches), and an exterior surface with functional surface groups. In this paper we determine generalised Randić, general Zagreb, general sum-connectivity indices of poly(propyl) ether imine, porphyrin, and zinc-Porphyrin dendrimers. We also compute ABC and GA indices of these families of dendrimers.

MSC 1991: Primary

References

[1] M. Saheli, H. Saati, and A. R. Ashrafi, Optoelectron. Adv. Mater. Rapid Commun. 4, 896 (2010).Search in Google Scholar

[2] H. J. Wiener, J. Am. Chem. Soc. 69, 17 (1947).10.1021/ja01193a005Search in Google Scholar

[3] M. Randić, J. Am. Chem. Soc. 97, 6609 (1975).10.1021/ja00856a001Search in Google Scholar

[4] I. Gutman and N. Trinajstić, Chem. Phys. Lett. 17, 535 (1972).10.1016/0009-2614(72)85099-1Search in Google Scholar

[5] A. T. Balaban, I. Motoc, D. Bonchev, and O. Mekenyan, Topics Curr. Chem. 114, 21 (1983).10.1007/BFb0111212Search in Google Scholar

[6] X. Li and H. Zhao, MATCH Commun. Math. Comput. Chem. 50, 57 (2004).Search in Google Scholar

[7] B. Zhou and N. Trinajstic, J. Math. Chem. 46, 1252 (2009).10.1007/s10910-008-9515-zSearch in Google Scholar

[8] B. Zhou and N. Trinajstic, J. Math. Chem. 47, 210 (2010).10.1007/s10910-009-9542-4Search in Google Scholar

[9] E. Estrada, L. Torres, L. Rodriguez, and I. Gutman, Indian J. Chem. 37, 849 (1998).Search in Google Scholar

[10] D. Vukicevic and B. Furtula, J. Math. Chem. 46, 1369 (2009).10.1007/s10910-009-9520-xSearch in Google Scholar

[11] A. Aslam, Y. Bashir, M. Rafiq, F. Haider, N. Muhammad, et al. Electr. J. Biol. 13, 94 (2017).Search in Google Scholar

[12] K. C. Das, I. Gutman, and B. Furtula, Chem. Phys. Lett. 511, 452 (2011).10.1016/j.cplett.2011.06.049Search in Google Scholar

[13] K. C. Das and S. Sorgun, MATCH Commun. Math. Comput. Chem. 72, 227 (2014).Search in Google Scholar

[14] K. C. Das, MATCH Commun. Math. Comput. Chem. 64, 619 (2010).Search in Google Scholar

[15] K. C. Das, I. Gutman, and B. Furtula, MATCH Commun. Math. Comput. Chem. 65, 595 (2011).Search in Google Scholar

[16] K. C. Das, I. Gutman, and B. Furtula, Discr. Appl. Math. 159, 2030 (2011).10.1016/j.dam.2011.06.020Search in Google Scholar

[17] W. Gao, L. Yan, and L. Shi, Optoelectr. Adv. Mater. Rapid Commun. 11, 119 (2017).Search in Google Scholar

[18] W. Gao, M. K. Siddiqui, M. Imran, M. K. Jamil, and M. R. Farahani, Saudi Pharma. J. 24, 258 (2016).10.1016/j.jsps.2016.04.012Search in Google Scholar PubMed PubMed Central

[19] W. Gao and W. F. Wang, J. Differ. Equ. Appl. 1 (2016), http://dx.doi.org/10.1080/10236198.2016.1197214.10.1080/10236198.2016.1197214Search in Google Scholar

[20] W. Gao and W. F. Wang, Chaos Soliton. Fract. 89, 290 (2016).10.1016/j.chaos.2015.11.035Search in Google Scholar

[21] W. Gao and M. R. Farahani, Appl. Math. Nonlinear Sci. 1, 99 (2016).10.21042/AMNS.2016.1.00009Search in Google Scholar

[22] X. Li and Y. Shi, Match Commun. Math. Comput. Chem. 59, 127 (2008).Search in Google Scholar

[23] X. Li, Y. Shi, and L. Wang, in: Recent Results in the Theory of Randic Index (Ed. B. F. I. Gutman), University of Kragujevac and Faculty of Science Kragujevac, 2008, p. 9.Search in Google Scholar

[24] H. S. Ramane and R. B. Jummannaver, Appl. Math. Nonlinear Sci. 1, 369 (2016).10.21042/AMNS.2016.2.00032Search in Google Scholar

[25] P. S. Ranjini, V. Lokesha, and I. N. Cangül, Appl. Math. Comput. 218, 6992 (2011).10.1016/j.amc.2011.03.125Search in Google Scholar

[26] M. S. Sardar, S. Zafar, and Z. Zahid, Appl. Math. Nonlinear Sci. 2, 83 (2017).10.21042/AMNS.2017.1.00007Search in Google Scholar

Received: 2017-3-8
Accepted: 2017-4-11
Published Online: 2017-5-22
Published in Print: 2017-5-24

©2017 Walter de Gruyter GmbH, Berlin/Boston

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