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The structure of sandpile groups of outerplanar graphs

Author

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  • Alfaro, Carlos A.
  • Villagrán, Ralihe R.

Abstract

We compute the sandpile groups of families of planar graphs having a common weak dual by evaluating the indeterminates of the critical ideals of the weak dual at the lengths of the cycles bounding the interior faces. This method allows us to determine the algebraic structure of the sandpile groups of outerplanar graphs, and can be used to compute the sandpile groups of many other planar graph families. Finally, we compute the identity element for the sandpile groups of the dual graphs of many outerplane graphs.

Suggested Citation

  • Alfaro, Carlos A. & Villagrán, Ralihe R., 2021. "The structure of sandpile groups of outerplanar graphs," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    • Handle: RePEc:eee:apmaco:v:395:y:2021:i:c:s0096300320308146
    DOI: 10.1016/j.amc.2020.125861
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    References listed on IDEAS

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    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. 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.
    3. Alfaro, Carlos A. & Lin, Jephian C.-H., 2019. "Critical ideals, minimum rank and zero forcing number," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 305-313.
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    Cited by:

    1. Alfaro, Carlos A. & Valencia, Carlos E. & Vargas, Marcos C., 2023. "Computing sandpile configurations using integer linear programming," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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