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Czechoslovak Mathematical Journal, Vol. 62, No. 4, pp. 1117-1134, 2012
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Some graphs determined by their (signless) Laplacian spectra

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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: ` liumuhuo@163.com`

**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

**Full text** available as PDF.

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