The critical group of \(K_m \times P_n\)

DOI10.1016/j.laa.2008.01.002zbMath1154.05038OpenAlexW2030280482MaRDI QIDQ924348

Yong-Liang Pan, Hao Liang, Jian Wang

Publication date: 15 May 2008

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

Full work available at URL: https://doi.org/10.1016/j.laa.2008.01.002

zbMATH Keywords

graphcritical groupLaplacian matrixinvariant factorSmith normal formtree number

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (6)

The sandpile group of a thick cycle graph ⋮ On the sandpile group of Eulerian series-parallel graphs ⋮ On the sandpile group of the cone of a graph ⋮ The critical group of \(K_{m} \times C_{n}\) ⋮ On the sandpile model of modified wheels. II ⋮ ON THE SANDPILE GROUP OF A FAMILY OF GRAPHS

Cites Work

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• On the sandpile group of the square cycle \(C^{2}_{n}\)
• A finite group attached to the laplacian of a graph
• Unimodular equivalence of graphs
• Chip-firing and the critical group of a graph
• The sand-pile model and Tutte polynomials
• Sandpile group on the graph \(\mathcal D_n\) of the dihedral group
• On the sandpile group of dual graphs
• The critical group of a threshold graph
• Algebraic Potential Theory on Graphs
• The lattice of integral flows and the lattice of integral cuts on a finite graph
• Critical groups for complete multipartite graphs and Cartesian products of complete graphs

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