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Counting spanning trees of a type of generalized Farey graphs

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  • Zhang, Jingyuan
  • Yan, Weigen

Abstract

The Farey graph Fn is derived from the famous Farey sequence and it is a small-world network with a connectivity distribution decaying exponentially. By using the Matrix-Tree theorem, Zhang et al. (2012) obtained the exact formula of the number of spanning trees of Fn. In this paper, by using the electrical network method, we consider a type of generalized Farey graphs and give the exact solution for the number of spanning trees of these generalized Farey graphs, which generalizes some previous results about the Farey graphs.

Suggested Citation

  • Zhang, Jingyuan & Yan, Weigen, 2020. "Counting spanning trees of a type of generalized Farey graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    • Handle: RePEc:eee:phsmap:v:555:y:2020:i:c:s0378437120303745
    DOI: 10.1016/j.physa.2020.124749
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    References listed on IDEAS

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    1. Zhang, Zhongzhi & Wu, Bin & Lin, Yuan, 2012. "Counting spanning trees in a small-world Farey graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3342-3349.
    2. Jia-Bao Liu & S. N. Daoud, 2019. "Number of Spanning Trees in the Sequence of Some Graphs," Complexity, Hindawi, vol. 2019, pages 1-22, March.
    3. Zhang, Zhongzhi & Rong, Lili & Guo, Chonghui, 2006. "A deterministic small-world network created by edge iterations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 567-572.
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    Cited by:

    1. Sun, Daoqiang & Li, Long & Liu, Kai & Wang, Hua & Yang, Yu, 2022. "Enumeration of subtrees of planar two-tree networks," Applied Mathematics and Computation, Elsevier, vol. 434(C).

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