General Sum-Connectivity Index with a = 1 for Trees and Unicyclic Graphs with k Pendants

Abstract

One of the newest molecular descriptors, the general sum-connectivity index of a graph G is defined as χ_α(G) = Σ_uvϵE(G)(d(u) + d(v))α, where d(u) denotes the degree of vertex u in G and is a real number. The aim of this paper is to determine the trees and the unicyclic graphs with k pendant vertices that maximize the general sum-connectivity index for α ≥ 1,with 2 ≤ k ≤ n for trees and 0 ≤ k ≤ n - 3 for unicyclic graphs.