Signless Laplacian energy of a graph and energy of a line graph

For a simple graph G of order n, size m and with signless Laplacian eigenvalues q1,q2,…,qn, the signless Laplacian energy QE(G) is defined as QE(G)=∑i=1n|qi−d‾|, where d‾=2mn is the average vertex degree of G. We obtain the lower bounds for QE(G), in terms of first Zagreb index M1(G), maximum degree d1, second maximum degree d2, minimum degree dn and second minimum degree dn−1. As a consequence of these bounds, we obtain several bounds for the energy E(L(G)) of the line graph L(G) of graph G in terms of various graph parameters like M1(G), ω (the clique number), n, m, etc., which improve some recently known bounds.