IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v359y2019icp107-120.html
   My bibliography  Save this article

Multi-distance granularity structural α-subtree index of generalized Bethe trees

Author

Listed:
  • Yang, Yu
  • Fan, Ai-wan
  • Wang, Hua
  • Lv, Hailian
  • Zhang, Xiao-Dong

Abstract

In graph theory and its applications, trees, BC-trees, subtrees and BC-subtrees have been extensively studied. We introduce a generalization of the BC-tree, called the multi-granular α-tree, which is a tree (of order at least α+1) where any two leaves are at a distance that is a multiple of α. We study the number of α-subtrees, through α-subtree generating functions, for generalized Bethe trees, Bethe trees and dendrimers (hyper-branched structures in molecular topology). Our results can also be used to examine the asymptotic behavior of the average order of α-subtrees in dendrimers.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:359:y:2019:i:c:p:107-120
    DOI: 10.1016/j.amc.2019.04.037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630031930325X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.04.037?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. 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.
    3. Liu, Guoliang & Liu, Guodong, 2018. "Wiener polarity index of dendrimers," Applied Mathematics and Computation, Elsevier, vol. 322(C), pages 151-153.
    4. Ghalavand, Ali & Reza Ashrafi, Ali, 2018. "Ordering chemical graphs by Randić and sum-connectivity numbers," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 160-168.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    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. 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.
    2. M. Kleshnina & K. Kaveh & K. Chatterjee, 2020. "The role of behavioural plasticity in finite vs infinite populations," Papers 2009.13160, arXiv.org.
    3. 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).
    4. Fulin Guo, 2023. "Experience-weighted attraction learning in network coordination games," Papers 2310.18835, arXiv.org.
    5. 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.
    6. 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.
    7. 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.
    8. 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).
    9. 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.
    10. Sarkar, Bijan, 2021. "The cooperation–defection evolution on social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    11. 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.
    12. Li, Bin-Quan & Wu, Zhi-Xi & Guan, Jian-Yue, 2022. "Critical thresholds of benefit distribution in an extended snowdrift game model," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    13. Sakiyama, Tomoko, 2021. "A power law network in an evolutionary hawk–dove game," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    14. Qi Su & Lei Zhou & Long Wang, 2019. "Evolutionary multiplayer games on graphs with edge diversity," PLOS Computational Biology, Public Library of Science, vol. 15(4), pages 1-22, April.
    15. Wang, Chaoqian & Szolnoki, Attila, 2023. "Inertia in spatial public goods games under weak selection," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    16. Mark Broom & Igor V. Erovenko & Jan Rychtář, 2021. "Modelling Evolution in Structured Populations Involving Multiplayer Interactions," Dynamic Games and Applications, Springer, vol. 11(2), pages 270-293, June.
    17. Brouard, Vianney & Pokalyuk, Cornelia, 2022. "Invasion of cooperative parasites in moderately structured host populations," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 221-263.
    18. Wang, Chaoqian & Lin, Zongzhe & Rothman, Dale S., 2022. "Public goods game on coevolving networks driven by the similarity and difference of payoff," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    19. Lv, Shaojie & Li, Jiaying & Zhao, Changheng, 2023. "The evolution of cooperation in voluntary public goods game with shared-punishment," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    20. Xiaochen Wang & Lei Zhou & Alex McAvoy & Aming Li, 2023. "Imitation dynamics on networks with incomplete information," Nature Communications, Nature, vol. 14(1), pages 1-11, December.

    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:eee:apmaco:v:359:y:2019:i:c:p:107-120. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.