For any real number alpha is an element of[0, 1], by the A(alpha)-matrix of a graph G we mean the matrix A(alpha) (G) = alpha D(G) + (1 - alpha)A(G), where A(G) and D(G) denote respectively the adjacency matrix and the diagonal matrix of vertex degrees of G. The largest eigenvalue of A(alpha)(G) is called the A(alpha)-index of G. Chang and Tam (2011) have proved that for every pair of integers n, k with -1
