On the general sum-connectivity index of trees

The general sum-connectivity index of a graph GG is defined as χα(G)=∑uv∈E(G)(du+dv)αχα(G)=∑uv∈E(G)(du+dv)α, where dudu denotes the degree of vertex uu in GG, E(G)E(G) denotes the edge set of GG, and αα is a real number. We determine the maximum value for the general sum-connectivity indices of nn-vertex trees and the corresponding extremal trees for α<α0α<α0, where α0=−4.3586…α0=−4.3586… is the unique root of the equation 4α−5α5α−6α=3.