Cacti with maximal general sum-connectivity index

Let V (G) and E(G) be, respectively, the vertex set and edge set of a graph G. The general sum-connectivity index of a graph G is denoted by chi(alpha)(G) and is defined as Sigma(uv is an element of E(G)) (d(u) + d(v))(alpha), where uv is an edge that connect the vertices u, V is an element of V (G), d(u) is the degree of a vertex u and alpha is any non-zero real number. A cactus is a graph in which any two cycles have at most one common vertex. Let l(n,t) denote the class of all cacti with order n and t pendant vertices. In this paper, a maximum general sum-connectivity index (chi(alpha) (G), alpha > 1) of a cacti graph with order n and t pendant vertices is considered. We determine the maximum general sum-connectivity index of n-vertex cacti graph. Based on our obtained results, we characterize the cactus with a perfect matching having the maximum general sum-connectivity index.

Automated summary

The paper discusses the general sum-connectivity index and related concepts, investigates the maximum general sum-connectivity index of cactus graphs, and characterizes cacti with a perfect matching having the maximum general sum-connectivity index.