Computing Some Eccentricity-Based Topological Indices of Para-Line Graphs of Hexagonal Cactus Chains

Abstract

Let $G=(V(G),E(G))$ be a simple molecular graph without directed and multiple edges and without loops. Graph theory has become an important component of the chemical mathematics, and it has become one of the most powerful mathematical tools in the analysis and study of the architecture of a chemical network. It studies of descriptors in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies in the chemistry science. There are a lot of topological indices in QSPR/QSAR studies. In this paper, some eccentricity-based topological indices namely the eccentric connectivity index ${\xi }^c(G),$ the modified eccentric connectivity index ${\xi }_c(G),$ the total eccentricity index $\xi (G),$ the second Zagreb eccentricity index $M_1^{**}(G)$ and the average eccentricity index $\mathit{avec}(G)$ are computed for the para-line graphs of some hexagonal cactus chains namely the para-chain $L_n,$ the ortho-chain $O_n$ and the meta-chain $M_n.$

Keywords:

• Chemical graph theory
• hexagonal cactus chains
• topological index
• eccentricity
• para-line graph

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 05C12
• 05C35
• 05C90
• 37F20
• 92E10

Acknowledgment

The authors are grateful to the editors and the anonymous referees for their constructive comments and valuable suggestions which have helped us very much to improve the paper.