On the maximum atom-bond sum-connectivity index of unicyclic graphs with given diameter

Abstract

Let $ G = (V(G), E(G)) $ be a simple connected graph with vertex set $ V(G) $ and edge set $ E(G) $. The atom-bond sum-connectivity (ABS) index was proposed recently and is defined as $ ABS(G) = \sum_{uv\in E(G)}\sqrt{\frac{d_{G}(u)+d_{G}(v)-2}{d_{G}(u)+d_{G}(v)}} $, where $ d_{G}(u) $ represents the degree of vertex $ u\in V(G) $. A connected graph $ G $ is called a unicyclic graph if $ |V(G)| = |E(G)| $. In this paper, we determine the maximum ABS index of unicyclic graphs with given diameter. In addition, the corresponding extremal graphs are characterized.

Keywords

• atom-bond sum-connectivity index
• unicyclic graph
• diameter
• pendent vertex