On the Sandpile group of the cone of a graph
Combinatorics
2012-03-01 v4
Abstract
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.
Cite
@article{arxiv.1004.3321,
title = {On the Sandpile group of the cone of a graph},
author = {Carlos A. Alfaro and Carlos E. Valencia},
journal= {arXiv preprint arXiv:1004.3321},
year = {2012}
}
Comments
20 pages, 11 figures. The title was changed, other impruvements were made throughout the article. To appear in Linear Algebra and Its Applications