IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i5p472-d234190.html
   My bibliography  Save this article

On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution

Author

Listed:
  • Yu Yang

    (School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
    School of Computer Science, Pingdingshan University, Pingdingshan 467000, China)

  • An Wang

    (School of Mathematics and Statistics Science, Pingdingshan University, Pingdingshan 467000, China)

  • Hua Wang

    (College of Software, Nankai University, Tianjin 300071, China
    Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA)

  • Wei-Ting Zhao

    (School of Computer Science, Pingdingshan University, Pingdingshan 467000, China)

  • Dao-Qiang Sun

    (School of Computer Science, Pingdingshan University, Pingdingshan 467000, China)

Abstract

The number of subtrees, or simply the subtree number, is one of the most studied counting-based graph invariants that has applications in many interdisciplinary fields such as phylogenetic reconstruction. Motivated from the study of graph surgeries on evolutionary dynamics, we consider the subtree problems of fan graphs, wheel graphs, and the class of graphs obtained from “partitioning” wheel graphs under dynamic evolution. The enumeration of these subtree numbers is done through the so-called subtree generation functions of graphs. With the enumerative result, we briefly explore the extremal problems in the corresponding class of graphs. Some interesting observations on the behavior of the subtree number are also presented.

Suggested Citation

  • Yu Yang & An Wang & Hua Wang & Wei-Ting Zhao & Dao-Qiang Sun, 2019. "On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution," Mathematics, MDPI, vol. 7(5), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:472-:d:234190
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/5/472/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/5/472/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Dale R. Fox, 1988. "Block cutpoint decomposition for markovian queueing systems," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 4(2), pages 101-114, June.
    3. Yang, Yu & Liu, Hongbo & Wang, Hua & Fu, Hongsun, 2015. "Subtrees of spiro and polyphenyl hexagonal chains," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 547-560.
    4. Zetina, Carlos Armando & Contreras, Ivan & Fernández, Elena & Luna-Mota, Carlos, 2019. "Solving the optimum communication spanning tree problem," European Journal of Operational Research, Elsevier, vol. 273(1), pages 108-117.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Li, Long & Yang, Yu & Hui, Zhi-hao & Jin, Bang-Bang & Wang, Hua & Fahad, Asfand & Zhang, Heng, 2024. "Algorithms for enumerating multiple leaf-distance granular regular α-subtree of unicyclic and edge-disjoint bicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 462(C).
    3. Yu Yang & Long Li & Wenhu Wang & Hua Wang, 2020. "On BC-Subtrees in Multi-Fan and Multi-Wheel Graphs," Mathematics, MDPI, vol. 9(1), pages 1-29, December.
    4. M. Kleshnina & K. Kaveh & K. Chatterjee, 2020. "The role of behavioural plasticity in finite vs infinite populations," Papers 2009.13160, arXiv.org.
    5. Renan Goetz & Jorge Marco, 2025. "Social networks, norm-enforcing ties and cooperation," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 20(2), pages 371-412, April.
    6. Arnaud Z. Dragicevic, 2025. "The Price Identity of Replicator(–Mutator) Dynamics on Graphs with Quantum Strategies in a Public Goods Game," Dynamic Games and Applications, Springer, vol. 15(1), pages 74-102, March.
    7. Li, Wen-Jing & Chen, Zhi & Jin, Ke-Zhong & Li, Lan & Yuan, Lin & Jiang, Luo-Luo & Perc, Matjaž & Kurths, Jürgen, 2022. "Eliminating poverty through social mobility promotes cooperation in social dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    8. Fulin Guo, 2023. "Experience-weighted attraction learning in network coordination games," Papers 2310.18835, arXiv.org.
    9. McAvoy, Alex & Fraiman, Nicolas & Hauert, Christoph & Wakeley, John & Nowak, Martin A., 2018. "Public goods games in populations with fluctuating size," Theoretical Population Biology, Elsevier, vol. 121(C), pages 72-84.
    10. Christopher Graser & Takako Fujiwara-Greve & Julián García & Matthijs van Veelen, 2025. "Repeated games with partner choice," PLOS Computational Biology, Public Library of Science, vol. 21(2), pages 1-19, February.
    11. Thomas Graham & Maria Kleshnina & Jerzy A. Filar, 2023. "Where Do Mistakes Lead? A Survey of Games with Incompetent Players," Dynamic Games and Applications, Springer, vol. 13(1), pages 231-264, March.
    12. Shiro Horiuchi, 2021. "Bridging of different sites by bohemians and tourists: analysis by agent-based simulation," Journal of Computational Social Science, Springer, vol. 4(2), pages 567-584, November.
    13. Yan, Zeyuan & Zhao, Hui & Liang, Shu & Li, Li & Song, Yanjie, 2024. "Inter-layer feedback mechanism with reinforcement learning boosts the evolution of cooperation in multilayer network," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    14. Wang, Qiushuang & Chen, Xiaojie & Szolnoki, Attila, 2025. "Coevolutionary dynamics of feedback-evolving games in structured populations," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
    15. Jiang, Zhi-Qiang & Wang, Peng & Ma, Jun-Chao & Zhu, Peican & Han, Zhen & Podobnik, Boris & Stanley, H. Eugene & Zhou, Wei-Xing & Alfaro-Bittner, Karin & Boccaletti, Stefano, 2023. "Unraveling the effects of network, direct and indirect reciprocity in online societies," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    16. Allen, Benjamin & McAvoy, Alex, 2024. "The coalescent in finite populations with arbitrary, fixed structure," Theoretical Population Biology, Elsevier, vol. 158(C), pages 150-169.
    17. Qi Su & Alexander J. Stewart, 2025. "Evolutionary dynamics of behavioral motivations for cooperation," Nature Communications, Nature, vol. 16(1), pages 1-12, December.
    18. Fabio Della Rossa & Fabio Dercole & Anna Di Meglio, 2020. "Direct Reciprocity and Model-Predictive Strategy Update Explain the Network Reciprocity Observed in Socioeconomic Networks," Games, MDPI, vol. 11(1), pages 1-28, March.
    19. Sarkar, Bijan, 2021. "The cooperation–defection evolution on social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    20. Peican Zhu & Xin Hou & Yangming Guo & Jiwei Xu & Jinzhuo Liu, 2021. "Investigating the effects of updating rules on cooperation by incorporating interactive diversity," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(2), pages 1-8, February.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:472-:d:234190. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.