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_۱,\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=۱}^{n}q_i^{k}, k\geqslant ۰, where q_۱,q_۲, \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.

Keywords:

Spectral moments sequence , signless Laplacian , generalized Petersen graph , T−order