Extremal atom-bond connectivity index of cactus graphs

Abstract

The atom-bond connectivity index of a graph G (ABC index for short) is defined as the summation of quantities √d(u)+d(v)-2/d(u)d(v) over all edges of G. A cactus graph is a connected graph in which every block is an edge or a cycle. The aim of this paper is to obtain the first and second maximum values of the ABC index among all n vertex cactus graphs.