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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 1 | Year 2021 | Article Id. IJMTT-V67I1P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I1P503

(a, b) - KA Indices of Benzenoid Systems and Phenylenes: The General Case


V.R.Kulli, Ivan Gutman
Abstract

In a recent paper by Kulli, two new vertex-degree-based (VDB) topological indices were put forward, called (a,b)-KA indices, depending on real-number parameters a and b. The majority of hitherto studied VDB indices are special cases of (a,b)-KA indices, for particular values of a and b. In this paper, we give generally valid expressions for (a,b)-KA indices of benzenoid systems and phenylenes, as well as of the respective coindices.

Keywords
Topological index, first (a, b)-KA index, second (a, b)-KA index, benzenoid system, phenylene.
References

[1] R.Todeschini and V. Consonni, Molecular Descriptors for Chemoinformatics, Wiley-VCH, Weinheim, (2009).
[2] V.R.Kulli, Graph indices, in: M. Pal, S. Samanta and A. Pal (eds.), Handbook of Research of Advanced Applications of Graph Theory in Modern Society, Global, Hershey, 66-91, (2020).
[3] V.R.Kulli, The (a, b)-KA indices of polycyclic aromatic hydrocarbons and benzenoid systems, International Journal of Mathematical Trends and Technology 65, 115-120, (2019).
[4] I.Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 ,535-538, (1972).
[5] M.Randić, On characterization of molecular branching, J. Am. Chem. Soc. 9 , 6609-6615,(1975).
[6] I.Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86, 11-16, (2021).
[7] I.Gutman and S. J. Cyvin, Introduction to the Theory of Benzenoid Hydrocarbons, Springer, Berlin, 1989.
[8] J.Rada, O. Araujo and I. Gutman, Randić index of benzenoid systems and phenylenes, Croat. Chem. Acta 74 (2001), 225-235.

Citation :

V.R.Kulli, Ivan Gutman, "(a, b) - KA Indices of Benzenoid Systems and Phenylenes: The General Case," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 1, pp. 17-20, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I1P503

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