On the general sum-connectivity index and general Randić index of cacti

Abstract

Let G be a connected graph. The degree of a vertex x of G, denoted by dG(x) , is the number of edges adjacent to x. The general sum-connectivity index is the sum of the weights (dG(x)+dG(y))α for all edges xy of G, where α is a real number. The general Randić index is the sum of weights of (dG(x)dG(y))α for all edges xy of G, where α is a real number. The graph G is a cactus if each block of G is either a cycle or an edge. In this paper, we find sharp lower bounds on the general sum-connectivity index and general Randić index of cacti.