On the maximum Laplacian Estrada index of graphs

Abstract

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,…,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)-graph for 3n−52<m≤2n−6 and the connected graph with r pendant vertices having maximum Laplacian Estrada index, respectively.