IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v392y2013i19p4584-4593.html
   My bibliography  Save this article

The Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs

Author

Listed:
  • Liao, Yunhua
  • Fang, Aixiang
  • Hou, Yaoping

Abstract

In this paper we recursively describe the Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs. In particular, we study the Abelian Sandpile Model on these graphs and obtain the generating function of the recurrent configurations. Further, we give some exact analytical expression for the Tutte polynomial at several special points

Suggested Citation

  • Liao, Yunhua & Fang, Aixiang & Hou, Yaoping, 2013. "The Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4584-4593.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:19:p:4584-4593
    DOI: 10.1016/j.physa.2013.05.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437113004445
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2013.05.021?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. Comellas, Francesc & Miralles, Alicia, 2009. "Modeling complex networks with self-similar outerplanar unclustered graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(11), pages 2227-2233.
    2. Majumdar, S.N. & Dhar, Deepak, 1992. "Equivalence between the Abelian sandpile model and the q→0 limit of the Potts model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 129-145.
    3. Comellas, Francesc & Miralles, Alícia & Liu, Hongxiao & Zhang, Zhongzhi, 2013. "The number of spanning trees of an infinite family of outerplanar, small-world and self-similar graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(12), pages 2803-2806.
    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. Alfaro, Carlos A. & Villagrán, Ralihe R., 2021. "The structure of sandpile groups of outerplanar graphs," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    2. Gong, Helin & Jin, Xian’an, 2014. "Potts model partition functions on two families of fractal lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 143-153.

    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. Sun, Bingbin & Yao, Jialing & Xi, Lifeng, 2019. "Eigentime identities of fractal sailboat networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 338-349.
    2. Wu, Xiaoxia & Zhang, Lianzhu & Chen, Haiyan, 2017. "Spanning trees and recurrent configurations of a graph," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 25-30.
    3. Antal A. Járai & Minwei Sun, 2021. "Asymptotic Height Distribution in High-Dimensional Sandpiles," Journal of Theoretical Probability, Springer, vol. 34(1), pages 349-362, March.
    4. Knor, Martin & Škrekovski, Riste, 2013. "Deterministic self-similar models of complex networks based on very symmetric graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4629-4637.
    5. Comellas, Francesc & Miralles, Alícia & Liu, Hongxiao & Zhang, Zhongzhi, 2013. "The number of spanning trees of an infinite family of outerplanar, small-world and self-similar graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(12), pages 2803-2806.
    6. Yinhu Zhai & Jia-Bao Liu & Shaohui Wang, 2017. "Structure Properties of Koch Networks Based on Networks Dynamical Systems," Complexity, Hindawi, vol. 2017, pages 1-7, March.
    7. Alfaro, Carlos A. & Villagrán, Ralihe R., 2021. "The structure of sandpile groups of outerplanar graphs," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    8. Liang, Jing & Zhao, Haixing & Yin, Jun & Xie, Sun, 2022. "Entropy and enumeration of spanning connected unicyclic subgraphs in self-similar network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    9. Miralles, Alicia & Comellas, Francesc & Chen, Lichao & Zhang, Zhongzhi, 2010. "Planar unclustered scale-free graphs as models for technological and biological networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1955-1964.
    10. Antal A. Járai & Nicolás Werning, 2014. "Minimal Configurations and Sandpile Measures," Journal of Theoretical Probability, Springer, vol. 27(1), pages 153-167, March.
    11. Xiao, Wenjun & Lin, Longxin & Chen, Guanrong, 2015. "Vertex-degree sequences in complex networks: New characteristics and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 437-441.

    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:phsmap:v:392:y:2013:i:19:p:4584-4593. 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.