On Laplacian energy of graphs

Let G be a graph with n vertices and m edges. Also let μ 1 , μ 2 , … , μ n − 1 , μ n = 0 be the eigenvalues of the Laplacian matrix of graph G . The Laplacian energy of the graph G is defined as L E = L E ( G ) = ∑ i = 1 n | μ i − 2 m n | . In this paper, we present some lower and upper bounds for L E of graph G in terms of n , the number of edges m and the maximum degree Δ . Also we give a Nordhaus–Gaddum-type result for Laplacian energy of graphs. Moreover, we obtain a relation between Laplacian energy and Laplacian-energy-like invariant of graphs.