On the Sandpile group of Dual graphs

Dominique Rossin (1) , Robert Cori (2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

The group of recurrent configurations in the sandpile model, introduced by Dhar, may be considered as a finite abelian group associated with any graph G; we call it the sandpile group of G. The aim of this paper is to prove that the sandpile group of planar graph is isomorphic to that of its dual. A combinatorial point of view on the subject is also developed.

Domaines: Combinatoire [math.CO]

Dominique Rossin, Robert Cori. On the Sandpile group of Dual graphs. European Journal of Combinatorics, 2000, 21, pp.447--459. ⟨hal-00016380⟩