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On the sandpile
group of Eulerian series-parallel graphs
Kyle Weishaar and James Seibert
Vol. 13 (2020), No. 3, 381–398
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Abstract |
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A sandpile configuration is a representation of the current layout of theoretical sand on a graph in which every vertex is assigned a nonnegative integer value. The Abelian sandpile group is a finite group composed of the recurrent sandpile configurations of a graph. We investigate the sandpile group of graphs constructed using the composition rules of series-parallel graphs, and determine the sandpile groups of parallel compositions of path-graphs. |
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Keywords
sandpile group, Eulerian graph, Laplacian, Smith normal
form
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Mathematical Subject Classification 2010
Primary: 05C50
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Milestones
Received: 29 April 2019
Revised: 27 April 2020
Accepted: 28 April 2020
Published: 14 July 2020
Communicated by Joshua Cooper
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Authors |
| Kyle Weishaar | |
| Department of Mathematics Regis University Denver, CO United States |
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| James Seibert | |
| Department of Mathematics Regis University Denver, CO United States |
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