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Given a graph $G$, if there is no nonisomorphic graph $H$ such that $G$ and $H$ have the same signless Laplacian spectra, then we say that $G$ is $Q$-DS. In this paper we show that every fan graph $F_n$ is $Q$-DS, where $F_n=K_1\vee P_{n-1}$ and $n\ge 3$.