Some Results on Laplacian Estrada Index of Graphs

Let G be a simple graph of order n and let mu(1)(G), mu(2)(G),..., mu(n) (G) be its Laplacian eigenvalues. The Laplacian Estrada index of G is defined as LEE(G) Sigma(n)(i=1)e(mu i(G)) In this paper, we present some new bounds for LEE(G) in terms of the number of vertices, the number of edges, the maximum degree, the minimum degree, the clique number, the independence number and the chromatic number of the graph G, and characterize the graphs for which the bounds are attained. In addition, we give an asymptotic property of LEE of iterated line graphs of a regular graph.