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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., 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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