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Enumeration of subtrees of planar two-tree networks

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Listed:
  • Sun, Daoqiang
  • Li, Long
  • Liu, Kai
  • Wang, Hua
  • Yang, Yu

Abstract

The number of subtrees, also referred to as the subtrees index, is a key parameter to measure graph structures such as networks. In this paper, we investigate the number of subtrees of planar two-tree networks. By “adding a virtual edge” and “edge orientation”, we present a linear time algorithm for computing the number of subtrees of planar two-tree networks, as well as a family of planar two-connected networks. As applications, we provide the formulae for the number of subtrees of the famous small-world Farey network and GDURT network. We also discuss the relationship between the spanning subtree number and the subtree number of these networks.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:434:y:2022:i:c:s0096300322004787
    DOI: 10.1016/j.amc.2022.127404
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    References listed on IDEAS

    as
    1. Xiao, Yuzhi & Zhao, Haixing, 2013. "New method for counting the number of spanning trees in a two-tree network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4576-4583.
    2. 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.
    3. Benjamin Allen & Gabor Lippner & Yu-Ting Chen & Babak Fotouhi & Naghmeh Momeni & Shing-Tung Yau & Martin A. Nowak, 2017. "Evolutionary dynamics on any population structure," Nature, Nature, vol. 544(7649), pages 227-230, April.
    4. 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.
    5. Xiao, Yuzhi & Zhao, Haixing & Hu, Guona & Ma, Xiujuan, 2014. "Enumeration of spanning trees in planar unclustered networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 236-243.
    6. 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).
    7. Yang, Yu & Fan, Ai-wan & Wang, Hua & Lv, Hailian & Zhang, Xiao-Dong, 2019. "Multi-distance granularity structural α-subtree index of generalized Bethe trees," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 107-120.
    8. Spiro, Sam, 2022. "The Wiener index of signed graphs," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    9. Lu, Zhe-Ming & Guo, Shi-Ze, 2012. "A small-world network derived from the deterministic uniform recursive tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 87-92.
    10. Yu, Guihai & Li, Xingfu & He, Deyan, 2022. "Topological indices based on 2- or 3-eccentricity to predict anti-HIV activity," Applied Mathematics and Computation, Elsevier, vol. 416(C).
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