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 $diag(d_1,cdots,d_n)$, where $d_i$ 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 $t_k(g)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ 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.