On the Sandpile group of the cone of a graph

Details On the Sandpile group of the cone of a graph On the Sandpile group of the cone of a graph

2010-04-19

arxiv.org/abs/1004.3321v4

Linear Algebra and Its Applications 436 5 (2012) 1154-1176

Mathematics

Combinatorics

20 pages, 11 figures. The title was changed, other impruvements were made throughout the article. To appear in Linear Algebra

Scientific paper

10.1016/j.laa.2011.07.030

In this article, we give a partial description of the sandpile group of the cone of the cartesian product of graphs in function of the sandpile group of the cone of their factors. Also, we introduce the concept of uniform homomorphism of graphs and prove that every surjective uniform homomorphism of graphs induces an injective homomorphism between their sandpile groups. As an application of these result we obtain an explicit description of a set of generators of the sandpile group of the cone of the hypercube of dimension d.

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