Signless Laplacian Spectral Characterization of Graphs with Isolated Vertices

A graph is said to be DQS if there is no other non-isomorphic graph with the same signless Laplacian spectrum. For a DQS graph $G$, we show that $G\cup rK_1$ is DQS under certain conditions. Applying these results, some DQS graphs with isolated vertices are obtained.