Trees of extremal connectivity index

The connectivity index wα(G)wα(G) of a graph G   is the sum of the weights (d(u)d(v))α(d(u)d(v))α of all edges uvuv of G  , where αα is a real number (α≠0)α≠0), and d(u)d(u) denotes the degree of the vertex u. Let T be a tree with n vertices and k   pendant vertices. In this paper, we give sharp lower and upper bounds for w1(T)w1(T). Also, for -1⩽α<0-1⩽α<0, we give a sharp lower bound and a upper bound for wα(T)wα(T).