Signless Laplacian spectral characterization of some graphs

Abstract

In this paper, we investigate (signless) Laplacian spectral characterization of graphs with star components. Also, we prove that the join graph $K_{n-\alpha }-e\vee \alpha K_1$ is $DQS$ for $n-\alpha >3$ and $\alpha \ne 3$, and for $\alpha =3$, we show that its only $Q$-cospectral mate is $\overline{K_{1,3}\cup K_2\cup (n-6)K_1}$.