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Document Type : Original Article

Authors

Department of Applied Mathematics, Semnan University, 35131-19111, Semnan, Iran

Abstract

Mathematical chemistry is a branch of theoretical chemistry that studies molecular structure without considering their quantum mechanics using mathematical methods. Carbon nanotubes are a particular type of fullerenes. In this article, K-Banhatti indices are obtained with the help of K-Banhatti polynomials for the molecular graph and the line graph of the TUC4C8(S) nanotube. Next, first, the (a, b)- Nirmala index is calculated for the molecular graph and line graph of TUC4C8(S) nanotube, and then using them, Y-index and some topological indices are computed.

Graphical Abstract

Analysis of K-Banhatti Polynomials and Calculation of Some Degree Based Indices Using (a, b)-Nirmala Index in Molecular Graph and Line Graph of TUC4C8(S) Nanotube

Keywords

Main Subjects

[1]. Kociak M., Kasumov A.Y., Guéron S., Reulet B., Khodos I.I., Gorbatov Y.B., Volkov V.T., Vaccarini L., Bouchiat H., Superconductivity in ropes of single-walled carbon nanotubes, Physical review letters, 2001, 86:2416 [Crossref], [Google scholar], [Publisher]
[2]. Iijima S., Helical microtubules of graphitic carbon, Nature, 1991, 354:56 [Crossref], [Google scholar], [Publisher]
[3]. Shin D.Y., Hussain S., Afzal F., Park C., Afzal D., Farahani M.R., Closed formulas for some new degree based topological descriptors using M-polynomial and boron triangular nanotube, Frontiers in Chemistry, 2021,‏ 8:613873 [Crossref], [Google scholar], [Publisher]
[4]. Ashrafi A.R., Yousefi S., Computing the Wiener index of a TUC4C8 (S) nanotorus, MATCH Communications in Mathematical and in Computer Chemistry, 2007, 57:403 [Google scholar], [Publisher]
[5]. Loghman A., Badakhshian L., PI polynomial of TUC4C8 (S) nanotubes and nanotorus, Digest Journal of Nanomaterials and Biostructures, 2009, 4:747 [Google scholar], [Publisher]
[6]. Gutman I., Trinajstic N., Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons, Chemical physics letters, 1972, 17:535 [Crossref], [Google scholar], [Publisher]
[7]. Alameri A., Al Naggar N., Al-Rumaima M., Alsharafi M., Y-index of some graph operations, International Journal of Applied Engineering Research, 2020, 15:173 [Crossref], [Google scholar], [Publisher]
[8]. Chu Z.Q., Salman M., Munir A., Khalid I., Rehman M.U., Liu J.B., Ali F., Some topological indices of dendrimers determined by their Banhatti polynomials, Heterocyclic Communications, 2020, 26:99 [Crossref], [Google scholar], [Publisher]
[9]. Kulli V.R., The (a,b) Nirmala index, International Journal of  engineering science & research Technology, 2022, 2:11 [Google scholar]
[10]. Gutman I., Geometric approach to degree-based topological indices: Sombor indices, MATCH Communications in Mathematical and in Computer Chemistr, 2021, 86:11 [Google scholar], [Publisher]
[11]. Zhou B., Trinajstić N., On a novel connectivity index, Journal of Mathematical Chemistry, 2009, 46:1252 [Crossref], [Google scholar], [Publisher]
[12]. Fajtlowicz S., On conjectures of Graffiti, Annals of Discrete Mathematics, 1988, 38:113 [Crossref], [Google scholar], [Publisher]
[13]. Vukičević D., Gašperov M., Bond additive modeling 1. Adriatic indices, Croatica chemica acta, 2010, 83:243 [Google scholar], [Publisher]
[14]. Kulli V.R., Nirmala index, International Journal of Mathematics Trends and Technology, 2021, 67:8 [Crossref], [Google scholar], [Publisher]
[15]. Eliasi M., Taeri B., Four new sums of graphs and their wiener indices, Discrete Applied Mathematics, 2009, 157:794 [Crossref], [Google scholar], [Publisher]