Investigation of Atom-Bond Connectivity Indices of Line Graphs Using Subdivision Approach

Abstract

A topological index is a numerical measure that characterises the whole structure of a graph. Based on vertex degrees, the idea of an atom-bond connectivity ABC index was introduced in chemical graph theory. Later, different versions of the ABC index were created, and some of these indices were recently designed. In this paper, we present the edge version of the atom-bond connectivity ABCe index, edge version of the multiplicative atom-bond connectivity ABCIIe index, and atom-bond connectivity temperature (ABCT) index for the line graph of subdivision graph of tadpole graph Tn,k, ladder graph Ln, and wheel graph Wn+1. Numerical simulation has also been shown for some novel families of atom-bond connectivity index comparing the three types of indices which can be useful for QSAR and QSPR studies.