A graph is determined by its signless Laplacian spectrum if no other non-isomorphic graph has the same signless Laplacian spectrum (simply $G$ is $DQS$). Let $T(a,b,c)$ denote the $T$-shape tree obtained by identifying the end vertices of three paths $P_{a+2}$, $P_{b+2}$ and $P_{c+2}$. We prove that its all line graphs $\mathcal {L}(T(a,b,c))$ except $\mathcal {L}(T(t,t,2t+1))$ ($t\geq 1$) are $DQS$, and determine the graphs which have the same signless Laplacian spectrum as $\mathcal {L}(T(t,t,2t+1))$. Let $\mu _1(G)$ be the maximum signless Laplacian eigenvalue of the graph $G$. We give the limit of $\mu _1(\mathcal {L}(T(a,b,c)))$, too.
Let $W_{n}=K_{1}\vee C_{n-1}$ be the wheel graph on $n$ vertices, and let $S(n,c,k)$ be the graph on $n$ vertices obtained by attaching $n-2c-2k-1$ pendant edges together with $k$ hanging paths of length two at vertex $v_{0}$, where $v_{0}$ is the unique common vertex of $c$ triangles. In this paper we show that $S(n,c,k)$ ($c\geq 1$, $k\geq 1$) and $W_{n}$ are determined by their signless Laplacian spectra, respectively. Moreover, we also prove that $S(n,c,k)$ and its complement graph are determined by their Laplacian spectra, respectively, for $c\geq 0$ and $k\geq 1$.