Maximum General Sum-Connectivity Index of Trees and Unicyclic Graphs with Given Order and Number of Pendant Vertices

For a∈R, the general sum-connectivity index of a graph G is defined as χa(G)=∑uv∈E(G)[dG(u)+dG(v)]a, where E(G) is the set of edges of G and dG(u) and dG(v) are the degrees of vertices u and v, respectively. For trees and unicyclic graphs with given order and number of pendant vertices, we present upper bounds on the general sum-connectivity index χa, where 0<a<1. We also present the trees and unicyclic graphs that attain the maximum general sum-connectivity index for 0<a<1.