on the aα-energy and aα-resolvent energy of graphs

Let g be a graph of order n. also, let a(g), and d(g) be the adjacency matrix and the diagonal matrixof the degrees of g, respectively. nikiforov defined the matrix aα(g) = αd(g) + (1 − α)a(g), where0 ≤ α ≤ 1. the resolvent energy of a graph g is defined as er(g) = pn i=0 n−1λi , where λ1; λ2; : : : ; λnare the eigenvalues of the adjacency matrix of g. in this paper we calculate energy and resolvent energyof aα(g) for some graph g.