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

Document Type : Research Paper

Authors

University of Kashan

Abstract

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 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 $T_k(G)=\sum_{i=1}^{n}q_i^{k}$, $k\geqslant 0$, 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.

Keywords

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