The structure of sandpile groups of outerplanar graphs

Carlos A. Alfaro and Ralihe R. Villagrán

Applied Mathematics and Computation, 2021, vol. 395, issue C

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.

Keywords: Sandpile group; Outerplanar graphs; Gröbner bases; Critical ideals; Spanning tree (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:395:y:2021:i:c:s0096300320308146

DOI: 10.1016/j.amc.2020.125861

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