Bounding the sum of powers of normalized Laplacian eigenvalues of a graph

Let G be a simple connected graph of order n. Its normalized Laplacian eigenvalues are lambda(1) > lambda(2) > ... >lambda(n-1) > lambda(n) = 0. In this paper, new bounds on S-beta*(G) = Sigma (i = 1) (n-1) lambda(beta)(i) (beta not equal 0.1) are derived. (C) 2017 Elsevier Inc. All rights reserved.