Zeroth-order general Randic index of trees with given order and distance conditions

The zeroth-order general Randic index of a graph G = (V, E) is defined as R-0(alpha)(G) = Sigma(v is an element of V)(d(v))(alpha) where d(v) is the degree of the vertex v is an element of V and a is a pertinently chosen real number. In this paper, we consider the trees with order n, diameter d or radius r, and extremal zeroth-order general Randic index. We obtain the trees with first three largest zeroth-order general Randic index among all the trees with order n, diameter d or radius r.