SIGNLESS LAPLACIAN SPECTRAL MOMENTS OF GRAPHS AND ORDERING SOME GRAPHS WITH RESPECT TO THEM

Let G=(V,E) be a simple graph. Denote by D(G) the diagonal matrix diag(d1,⋯,dn), where di is the degree of vertex i and A(G) the adjacency matrix of G. The signless Laplacian matrix of G is Q(G)=D(G)+A(G) and the k−th signless Laplacian spectral moment of graph G is defined as Tk(G)=∑ni=1qki, k⩾0, where q1,q2, ⋯, qn are the eigenvalues of the signless Laplacian matrix of G. In this paper we first compute the k−th signless Laplacian spectral moments of a graph for small k and then we order some graphs with respect to the signless Laplacian spectral moments.