On zeroth-order general Randic indices of trees and unicyclic graphs

Let C be a graph with vertex set V(G). The zeroth-order general Randic index of G is defined as [GRAPHICS] where d(v) is the degree of the vertex v in G and a is a real number. For alpha > I or alpha < 0, we characterize respectively the n-vertex trees and the n-vertex unicyclic graphs of fixed number of pendent vertices with the first three largest zeroth-order general Randic indices, and we also characterize respectively the n-vertex trees and the n-vertex unicyclic graphs of fixed maximum degree with the first two largest zeroth-order general Randic indices.