On the sandpile group of the cone of a graph

DOI10.1016/j.laa.2011.07.030zbMath1236.05131arXiv1004.3321OpenAlexW2106963958MaRDI QIDQ665936

Carlos E. Valencia, Carlos A. Alfaro

Publication date: 7 March 2012

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.3321

zbMATH Keywords

hypercubegraph homomorphismcritical groupCartesian productsandpile group

Mathematics Subject Classification ID

Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items (21)

The distribution of sandpile groups of random graphs ⋮ Small clique number graphs with three trivial critical ideals ⋮ Graphs with few trivial critical ideals ⋮ The sandpile group of polygon rings and twisted polygon rings ⋮ Chip-firing groups of iterated cones ⋮ Graphs with real algebraic co-rank at most two ⋮ On graphs with 2 trivial distance ideals ⋮ The structure of sandpile groups of outerplanar graphs ⋮ On the Jacobian group of a cone over a circulant graph ⋮ Counting spanning trees of \((1, N\))-periodic graphs ⋮ Chip-Firing Games and Critical Groups ⋮ Digraphs with at most one trivial critical ideal ⋮ Computing the degree of a lattice ideal of dimension one ⋮ Sandpile groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields ⋮ Graphs with few trivial characteristic ideals ⋮ Enumeration of cospectral and coinvariant graphs ⋮ Critical ideals of signed graphs with twin vertices ⋮ Critical ideals, minimum rank and zero forcing number ⋮ ON THE SANDPILE GROUP OF A FAMILY OF GRAPHS ⋮ Distance ideals of graphs ⋮ The sandpile group of a polygon flower

Cites Work

• Unnamed Item
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• The critical groups of a family of graphs and elliptic curves over finite fields
• On the sandpile group of regular trees
• The critical group of \(K_m \times P_n\)
• Smith normal form and Laplacians
• The sandpile group of a tree
• Arithmetical graphs
• A finite group attached to the laplacian of a graph
• Unimodular equivalence of graphs
• Asymmetric Abelian sandpile models
• Chip-firing and the critical group of a graph
• Problems in algebraic combinatorics
• On the critical group of the \(n\)-cube
• On the sandpile group of dual graphs
• The critical group of a threshold graph
• On the identity of the sandpile group
• The critical group of a line graph
• On the sandpile group of \(P_{4}\times C_n\)
• On the sandpile group of the graph \(K_{3}\times C_n\)
• Self-organized criticality
• Harmonic Morphisms and Hyperelliptic Graphs
• Chip-Firing and Rotor-Routing on Directed Graphs
• Bicycles and Spanning Trees
• Algebraic Potential Theory on Graphs
• Critical groups for complete multipartite graphs and Cartesian products of complete graphs
• Self-organized critical state of sandpile automaton models
• Explicit characterization of the identity configuration in an Abelian sandpile model

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