The Laplacian energy and Laplacian Estrada index of random multipartite graphs

Let G be a simple graph on n vertices and m edges and mu(1), mu(2), ..., mu(3) be the eigenvalues of the Laplacian matrix of G. The Laplacian energy of G is defined as epsilon(L)(G) = Sigma(n)(i=1) vertical bar mu(i) - 2m/n vertical bar and the Laplacian Estrada index of G is defined as LEE(G) = Sigma(n)(i=1) e(mu i-2m/n). In this paper we establish asymptotic lower and upper bounds to the Laplacian energy and Laplacian Estrada index, respectively, for random multipartite graphs. (C) 2016 Elsevier Inc. All rights reserved.