Laplacian energy of a graph

Let G be a graph with n vertices and m edges. Let lambda(1), lambda(2) - - lambda(n) be the eigenvalues of the adjacency matrix of G, and let mu(1), mu(2) .....,mu(n) be the eigenvalues of the Laplacian matrix of G. An earlier much studied quantity E(G) = Sigma(n)(i) = 1 vertical bar lambda(i)vertical bar is the energy of the graph G. We now define and investigate the Laplacian energy as LE(G) = Sigma(n)(i) = vertical bar mu(i) - 2m/n vertical bar. There is a great deal of analogy between the properties of E(G) and LE(G), but also some significant differences. (c) 2005 Elsevier Inc. All rights reserved.