Vol. 13, No. 3, 2020

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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
Abstract

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
Mathematical Subject Classification 2010
Primary: 05C50
Milestones
Received: 29 April 2019
Revised: 27 April 2020
Accepted: 28 April 2020
Published: 14 July 2020

Communicated by Joshua Cooper
Authors
Kyle Weishaar
Department of Mathematics
Regis University
Denver, CO
United States
James Seibert
Department of Mathematics
Regis University
Denver, CO
United States