Some graphs determined by their (signless) Laplacian spectra

Let Wn = K1 ∀ Cn−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 υ0, where υ0 is the unique common vertex of c triangles. In this paper we show that S(n, c, k) (c ⩾ 1, k ⩾ 1) and Wn 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 ⩾ 0 and k ⩾ 1.