Relation between energy and (signless) Laplacian energy of graphs

Let G = (V, E) be a simple graph of order n with m edges. Also let E(G), LE(G) and LE⁺(G) be energy, Laplacian energy and signless Laplacian energy of graph G, respectively. In this paper, we obtain a relation between E(G), LE(G) and LE⁺(G) of graph G. Moreover, we present an upper bound on E(G) of graph G in terms of m and rank r.