The general Randić index of trees with given number of pendent vertices

The general Randić index of a graph G is defined as Rα(G)=∑uv∈E(G)(d(u)d(v))α, where d(u) denotes the degree of a vertex u in G and α is a real number. In this paper, we determine the maximum general Randić indices of trees and chemical trees with n vertices and k pendent vertices for 4≤k≤⌊n+23⌋ and α0 ≤ α < 0, where α0≈−0.5122 is the unique non-zero root of the equation 6·4α−20·9α+10·12α−16α+5·24α=0. The corresponding extremal graphs are also characterized.