On the Sandpile group of the cone of a graph

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.

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

References in corpus (2)

• The Abelian sandpile; a mathematical introduction
• Explicit characterization of the identity configuration in an Abelian Sandpile Model

Cited by in corpus (11)

• The distribution of sandpile groups of random graphs
• Computing the degree of a lattice ideal of dimension one
• Graph classes for critical ideals, minimum rank and zero forcing number
• Sandpile groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields
• Chip-Firing Games and Critical Groups
• Counting Finite Index Subrings of ${\mathbb{Z}}^n$
• Critical groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields: an extended abstract
• Degree and algebraic properties of lattice and matrix ideals
• The sandpile group of a polygon flower
• Digraphs with at most one trivial critical ideal
• Enumeration of cospectral and coinvariant graphs