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The number of spanning trees of an infinite family of outerplanar, small-world and self-similar graphs

Author

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  • Comellas, Francesc
  • Miralles, Alícia
  • Liu, Hongxiao
  • Zhang, Zhongzhi

Abstract

In this paper we give an exact analytical expression for the number of spanning trees of an infinite family of outerplanar, small-world and self-similar graphs. This number is an important graph invariant related to different topological and dynamic properties of the graph, such as its reliability, synchronization capability and diffusion properties. The calculation of the number of spanning trees is a demanding and difficult task, in particular for large graphs, and thus there is much interest in obtaining closed expressions for relevant infinite graph families. We have also calculated the spanning tree entropy of the graphs which we have compared with those for graphs with the same average degree.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:12:p:2803-2806
    DOI: 10.1016/j.physa.2012.10.047
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    References listed on IDEAS

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    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. Ramon Ferrer i Cancho & Christiaan Janssen & Ricard V. Solé, 2001. "The Topology of Technology Graphs: Small World Patterns in Electronic Circuits," Working Papers 01-05-029, Santa Fe Institute.
    3. Yuhai Tu, 2000. "How robust is the Internet?," Nature, Nature, vol. 406(6794), pages 353-354, July.
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    Citations

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    Cited by:

    1. 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.
    2. Alfaro, Carlos A. & Villagrán, Ralihe R., 2021. "The structure of sandpile groups of outerplanar graphs," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    3. 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.
    4. 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).

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