Characterizing graphs with maximal Laplacian Estrada index

Let G be a simple graph on n vertices. The Laplacian Estrada index of G   is defined as LEE(G)=∑i=1neμi, where μ1,μ2,…,μnμ1,μ2,…,μn are the Laplacian eigenvalues of G  . In this paper, we give some upper bounds for the Laplacian Estrada index of graphs and characterize the connected (n,m)(n,m)-graphs for n+1≤m≤3n−52 and the graphs of given chromatic number having maximum Laplacian Estrada index, respectively.