On the sandpile group of Eulerian series-parallel graphs

Weishaar, Kyle; Seibert, James

doi:10.2140/involve.2020.13.381

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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

DOI: 10.2140/involve.2020.13.381

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.

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

Vol. 13, No. 3, 2020