The Laplacian energy and Laplacian Estrada index of random multipartite graphs

Let G be a simple graph on n vertices and m   edges and μ1,μ2,…,μnμ1,μ2,…,μn be the eigenvalues of the Laplacian matrix of G. The Laplacian energy of G   is defined as EL(G)=∑i=1n|μi−2m/n| and the Laplacian Estrada index of G   is defined as LEE(G)=∑i=1neμi−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.