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Some graphs determined by their (signless) Laplacian spectra

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Abstract

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.

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Authors and Affiliations

  1. Department of Applied Mathematics, South China Agricultural University, Guangzhou, 510642, P.R. China

    Muhuo Liu

  2. School of Mathematical Science, Nanjing Normal University, Nanjing, 210097, P.R. China

    Muhuo Liu

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  1. Muhuo Liu
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Correspondence to Muhuo Liu.

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Liu, M. Some graphs determined by their (signless) Laplacian spectra. Czech Math J 62, 1117–1134 (2012). https://doi.org/10.1007/s10587-012-0067-9

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  • DOI: https://doi.org/10.1007/s10587-012-0067-9

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