  {Signless Laplacian determinations of some graphs with independent edges}%
{Let $G$ be a simple undirected graph. Then the signless Laplacian matrix of
$G$ is defined as $D_G + A_G$ in which $D_G$ and $A_G$ denote the degree matrix
and the adjacency matrix of $G$, respectively. The graph $G$ is said to be
determined by its signless Laplacian spectrum ({\rm DQS}, for short), if any
graph having the same signless Laplacian spectrum as $G$ is isomorphic to $G$.
We show that $G\sqcup rK_2$ is determined by its signless Laplacian spectra
under certain conditions, where $r$ and $K_2$ denote a natural number and the
complete graph on two vertices, respectively. Applying these results, some {\rm
DQS} graphs with independent edges are obtained.

Combinatorics