Chip-Firing and the Critical Group of a Graph

Authors:
N. L. Biggs
Affiliations:
London School of Economics, Department of Mathematics, Center for Discrete & Applied Math, Houghton Street WC2A 2AE, London, UK. N.L.Biggs@lse.ac.uk
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
1999

Citing 4
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Abstract

A variant of the chip-firing game on a graph is defined. It is shown that the set of configurations that are stable and recurrent for this game can be given the structure of an abelian group, and that the order of the group is equal to the tree number of the graph. In certain cases the game can be used to illuminate the structure of the group.