On Laplacian energy of graphs

Let GG be a graph with nn vertices and mm edges. Also let μ1,μ2,…,μn−1,μn=0μ1,μ2,…,μn−1,μn=0 be the eigenvalues of the Laplacian matrix of graph GG. The Laplacian energy of the graph GG is defined as LE=LE(G)=∑i=1n|μi−2mn|. In this paper, we present some lower and upper bounds for LELE of graph GG in terms of nn, the number of edges mm and the maximum degree ΔΔ. 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.