Czechoslovak Mathematical Journal, Vol. 62, No. 4, pp. 1117-1134, 2012

Some graphs determined by their (signless) Laplacian spectra

Muhuo Liu

M. Liu, Department of Applied Mathematics, South China Agricultural University, Guangzhou, 510642, P. R. China, and School of Mathematical Science, Nanjing Normal University, Nanjing, 210097, P. R. China, e-mail:

Abstract: 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 $S(n,c,k)$ ($c\geq1$, $k\geq1$) 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 $c\geq0$ and $k\geq1$.

Keywords: Laplacian spectrum, signless Laplacian spectrum, complement graph

Classification (MSC 2010): 05C50, 15A18

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