On the maximum general sum-connectivity index of trees with a fixed order and maximum degree

Abstract

The general sum-connectivity index of a graph [Formula: see text], denoted by [Formula: see text], is defined as [Formula: see text], where [Formula: see text] is the edge connecting the vertices [Formula: see text], [Formula: see text] denotes the degree of the vertex [Formula: see text], and [Formula: see text] is a nonzero real number. This paper is devoted to characterizing the graphs having the maximal [Formula: see text] value among all the trees with order [Formula: see text] and fixed maximum degree.