On the general sum-connectivity index of trees

The general sum-connectivity index of a graph G is defined as χ α ( G ) = ∑ u v ∈ E ( G ) ( d u + d v ) α , where d u denotes the degree of vertex u in G , E ( G ) denotes the edge set of G , and α is a real number. We determine the maximum value for the general sum-connectivity indices of n -vertex trees and the corresponding extremal trees for α < α 0 , where α 0 = − 4.3586 … is the unique root of the equation 4 α − 5 α 5 α − 6 α = 3 .