The critical group of \(K_{m} \times C_{n}\)

DOI10.1007/s10114-011-9063-5zbMath1222.05181arXiv0912.3609OpenAlexW1970148308MaRDI QIDQ546283

Jun-Ming Xu, Jian Wang, Yong-Liang Pan

Publication date: 24 June 2011

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.3609

zbMATH Keywords

graphcritical groupLaplacian matrixinvariant factorSmith normal formtree number

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (2)

On Jacobian group and complexity of the generalized Petersen graph \(\mathrm{GP}(n,k)\) through Chebyshev polynomials ⋮ The sandpile group of a thick cycle graph

Cites Work

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