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

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) = uvEE(G) dG(u)+dG(v) , where dG(u) represents the degree of vertex u E 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.