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On the Laplacian spectral characterization of Π-shape trees

Author

Listed:
  • Fei Wen

    (Lanzhou Jiaotong University)

  • Qiongxiang Huang

    (Xinjiang University)

  • Xueyi Huang

    (Xinjiang University)

  • Fenjin Liu

    (Chang’an University)

Abstract

A Π-shape tree is a tree with exactly two vertices having the maximum degree three. In this paper, we classify the Π-shape trees into two types, and complete the spectral characterization for one type. Exactly, we prove that all graphs of this type are determined by their Laplacian spectra with some exceptions. Moreover, we give some L-cospectral mates of some graphs for another type.

Suggested Citation

  • Fei Wen & Qiongxiang Huang & Xueyi Huang & Fenjin Liu, 2018. "On the Laplacian spectral characterization of Π-shape trees," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(3), pages 397-411, September.
    • Handle: RePEc:spr:indpam:v:49:y:2018:i:3:d:10.1007_s13226-018-0276-5
    DOI: 10.1007/s13226-018-0276-5
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    References listed on IDEAS

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    1. van Dam, E.R. & Haemers, W.H., 2009. "Developments on spectral characterizations of graphs," Other publications TiSEM 7b5eb8d4-dfc2-4392-bb3f-4, Tilburg University, School of Economics and Management.
    2. van Dam, E.R. & Haemers, W.H., 2003. "Which graphs are determined by their spectrum?," Other publications TiSEM a9a1857e-13ce-4da7-bcca-b, Tilburg University, School of Economics and Management.
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