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 $\left(ABC\right)$ 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 $\left(AB{C}_e\right)$ index, edge version of the multiplicative atom-bond connectivity $\left(ABCI{I}_e\right)$ index, and atom-bond connectivity temperature ( $ABCT$ ) index for the line graph of subdivision graph of tadpole graph $\left(T_{n,k}\right)$ , ladder graph $\left(L_n\right)$ , and wheel graph $\left(W_{n+1}\right)$ . 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.