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 laplacianmatrix 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.