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Spectral analysis for a family of treelike networks

Author

Listed:
  • Dai, Meifeng
  • Wang, Xiaoqian
  • Chen, Yufei
  • Zong, Yue
  • Sun, Yu
  • Su, Weiyi

Abstract

For a network, knowledge of its Laplacian eigenvalues is central to understand its structure and dynamics. In this paper, we study the Laplacian spectra and their applications for a family of treelike networks. Firstly, in order to obtain the Laplacian spectra, we calculate the constant term and monomial coefficient of characteristic polynomial of the Laplacian matrix for a family of treelike networks. By using the Vieta theorem, we then obtain the sum of reciprocals of all nonzero eigenvalues of Laplacian matrix. Finally, we determine some interesting quantities that are related to the sum of reciprocals of all nonzero eigenvalues of Laplacian matrix, such as Kirchhoff index, global mean-first passage time (GMFPT).

Suggested Citation

  • Dai, Meifeng & Wang, Xiaoqian & Chen, Yufei & Zong, Yue & Sun, Yu & Su, Weiyi, 2018. "Spectral analysis for a family of treelike networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1-6.
  • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:1-6
    DOI: 10.1016/j.physa.2018.02.088
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    Cited by:

    1. Wang, Daohua & Zeng, Cheng & Zhao, Zixuan & Wu, Zhiqiang & Xue, Yumei, 2023. "Kirchhoff index of a class of polygon networks," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Heidrich Balázs & Csákné Filep Judit & Mosolygó-Kiss Ágnes, 2018. "The war of the worlds? – A passing and taking of succession in Hungarian family businesses," Prosperitas, Budapest Business University, vol. 5(3), pages 8-23.

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