The structure of sandpile groups of outerplanar graphs

•We did a general review of the manuscript checking grammar and typos suggested by reviewers.•We have added three SAGE codes suggested by Reviewer #1.•Reviewer #1 suggested to include statistics comparing the codes with other computer algebra system. However, we consider that this goes beyond the ai...

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Bibliographic Details
Published in:Applied mathematics and computation 2021-04, Vol.395, p.125861, Article 125861
Main Authors: Alfaro, Carlos A., Villagrán, Ralihe R.
Format: Article
Language:English
Subjects:
Critical ideals
Gröbner bases
Outerplanar graphs
Sandpile group
Spanning tree
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Summary:•We did a general review of the manuscript checking grammar and typos suggested by reviewers.•We have added three SAGE codes suggested by Reviewer #1.•Reviewer #1 suggested to include statistics comparing the codes with other computer algebra system. However, we consider that this goes beyond the aim of our manuscript since our objective is not focus on the performance of our algorithms, rather we are introducing a methodology to compute the algebraic and combinatorial structure of outerplanar graphs. 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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2020.125861