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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Micah Henson
Department of Applied Mathematics, University of Washington
Electrical & Electronics Engineering

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The sandpile group of a thick cycle graph Diane Christine Alar; Jonathan Celaya; Luis David Garcia Puente; Micah Henson; Ashley K. Wheeler
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2022.10.2.20

Abstract

The majority of graphs whose sandpile groups are known are either regular or simple. We give an explicit formula for a family of non-regular multi-graphs called thick cycles. A thick cycle graph is a cycle where multi-edges are permitted. Its sandpile group is the direct sum of cyclic groups of orders given by quotients of greatest common divisors of minors of its Laplacian matrix. We show these greatest common divisors can be expressed in terms of monomials in the graph’s edge multiplicities.
Co-Authors Ashley K. Wheeler Diane Christine Alar Jonathan Celaya Luis David Garcia Puente