ON THE $M$-POLYNOMIAL AND SOME TOPOLOGICAL INDICES OF THE PARA-LINE GRAPHS OF THE NANOSTRUCTURE $TUC_4C_8(R)$

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 248

Volume : 17 , Issue : 3
DOI:
Author :
Narahari N. Swamy (Department of Mathematics, University College of Science, Tumkur University, Tumakuru - 572103, Karnataka, INDIA)
Chandan K. G. (Department of Mathematics, University College of Science, Tumkur University, Tumakuru - 572103, Karnataka, INDIA)
B. Sooryanarayana (Department of Mathematical and Computational Studies, Dr. Ambedkar Institute of Technology, Bengaluru - 560056, Karnataka, INDIA)

Abstract

The study of topological indices associated with molecular graphs is very helpful in understanding many of their physico-chemical properties. Various degree based topological indices such as generalized Randi$\acute{c}$ index, Zagreb index, Arithmetic-Geometric index and harmonic index are found to be particularly useful in the study of many molecular nanostructures. In this paper, we obtain the $M$-polynomial of the para-line graphs of the $2D$-lattice, nanotube and nanotorus of $TUC_4C_8(R)\left[p,q\right]$, by means of which, we compute some of their topological indices.

Keywords and Phrases

Topological indices, subdivision, para-line graph, $M$-polynomial, $2D$-lattice, nanotube, nanotorus.

A.M.S. subject classification

05C09, 05C31, 92E10.

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