Some graphs determined by their (signless) Laplacian spectra

Let W _n = K ₁ ? 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 υ ₀, where υ ₀ is the unique common vertex of c triangles. In this paper we show that S(n, c, k) (c ? 1, k ? 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 ? 0 and k ? 1.