On generalized atom-bond connectivity index of cacti

Document Type: Research Paper

Author

School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China

10.22052/ijmc.2019.195759.1456

Abstract

The generalized atom-bond connectivity index of a graph G is denoted by ABCa(G) and defined as the sum of weights ((d(u)+d(v)-2)/d(u)d(v))aa$ over all edges uv∊G. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, we compute sharp bounds for  ABCa index for cacti of order $n$ with fixed number of cycles and for cacti of order $n$ with given number of pendant vertices. Furthermore, we identify all the cacti that achieve the bounds.

Keywords


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