The structure of sandpile groups of outerplanar graphs

Carlos A. Alfaro; Ralihe R. Villagrán

doi:10.1016/j.amc.2020.125861

The structure of sandpile groups of outerplanar graphs

Carlos A. Alfaro (Corresponding author)
, Ralihe R. Villagrán

Research output: Contribution to journal › Article › Academic › peer-review

6 Citations (Scopus)

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.

Original language	English
Article number	125861
Number of pages	18
Journal	Applied Mathematics and Computation
Volume	395
DOIs	https://doi.org/10.1016/j.amc.2020.125861
Publication status	Published - 15 Apr 2021
Externally published	Yes

Bibliographical note

Funding Information:
This research was partially supported by SNI and CONACyT. The authors are grateful to Prof. H.J. Fleischner for sending the authors some of his papers.

Funding

This research was partially supported by SNI and CONACyT. The authors are grateful to Prof. H.J. Fleischner for sending the authors some of his papers.

Keywords

Critical ideals
Gröbner bases
Outerplanar graphs
Sandpile group
Spanning tree

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10.1016/j.amc.2020.125861

Cite this

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title = "The structure of sandpile groups of outerplanar graphs",

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 = "Critical ideals, Gr{\"o}bner bases, Outerplanar graphs, Sandpile group, Spanning tree",

author = "Alfaro, \{Carlos A.\} and Villagr{\'a}n, \{Ralihe R.\}",

note = "Funding Information: This research was partially supported by SNI and CONACyT. The authors are grateful to Prof. H.J. Fleischner for sending the authors some of his papers. ",

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T1 - The structure of sandpile groups of outerplanar graphs

AU - Alfaro, Carlos A.

AU - Villagrán, Ralihe R.

N1 - Funding Information: This research was partially supported by SNI and CONACyT. The authors are grateful to Prof. H.J. Fleischner for sending the authors some of his papers.

PY - 2021/4/15

Y1 - 2021/4/15

N2 - 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.

AB - 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.

KW - Critical ideals

KW - Gröbner bases

KW - Outerplanar graphs

KW - Sandpile group

KW - Spanning tree

UR - https://www.scopus.com/pages/publications/85098687300

U2 - 10.1016/j.amc.2020.125861

DO - 10.1016/j.amc.2020.125861

M3 - Article

AN - SCOPUS:85098687300

SN - 0096-3003

VL - 395

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 125861

ER -

The structure of sandpile groups of outerplanar graphs

Abstract

Bibliographical note

Funding

Keywords

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