### The sandpile group of a thick cycle graph

#### Abstract

*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.

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PDFDOI: http://dx.doi.org/10.5614/ejgta.2022.10.2.20

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