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The spectral characterization of wind-wheel graphs

Author

Listed:
  • Fei Wen

    (Xinjiang University)

  • Qiongxiang Huang

    (Xinjiang University)

  • Xueyi Huang

    (Xinjiang University)

  • Fenjin Liu

    (Chang’an University)

Abstract

Let G s,t denote the wind-wheel graph on n vertices obtained by appending s triangle(s) to a pendant vertex of a path P t+1 with just a vertex in common. In this paper, we prove that all wind-wheel graphs are determined by their Laplacian spectra as well as signless Laplacian spectra. As G s,t is the well-known friendship graph if t = 0, our results include that the friendship graph is determined by its Laplacian spectrum as well as signless Laplacian spectrum, which provides of a new proofs of the results in [15].

Suggested Citation

  • Fei Wen & Qiongxiang Huang & Xueyi Huang & Fenjin Liu, 2015. "The spectral characterization of wind-wheel graphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(5), pages 613-631, October.
    • Handle: RePEc:spr:indpam:v:46:y:2015:i:5:d:10.1007_s13226-015-0141-8
    DOI: 10.1007/s13226-015-0141-8
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    References listed on IDEAS

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    1. van Dam, E.R. & Haemers, W.H., 2007. "Developments on Spectral Characterizations of Graphs," Discussion Paper 2007-33, Tilburg University, Center for Economic Research.
    2. van Dam, E.R. & Haemers, W.H., 2002. "Which Graphs are Determined by their Spectrum?," Discussion Paper 2002-66, Tilburg University, Center for Economic Research.
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    Cited by:

    1. Xihe Li & Ligong Wang & Shangyuan Zhang, 2018. "The Signless Laplacian Spectral Radius of Some Strongly Connected Digraphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(1), pages 113-127, March.

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