Plans' periodicity theorem for Jacobian of circulant graphs

DOI10.1134/S1064562421030121zbMath1477.57007MaRDI QIDQ2243871

Alexander Mednykh, Ilya A. Mednykh

Publication date: 11 November 2021

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

knotAlexander polynomialhomology groupcritical groupcyclic coveringcirculant graphknot branched covering

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Relations of low-dimensional topology with graph theory (57M15) Knot theory (57K10)

Related Items (2)

Counting rooted spanning forests for circulant foliation over a graph ⋮ Cyclic coverings of graphs. Counting rooted spanning forests and trees, Kirchhoff index, and Jacobians

Cites Work

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• On the structure of the Jacobian group for circulant graphs
• Complexity of discrete Seifert foliations over a graph
• On Jacobian group and complexity of the generalized Petersen graph \(\mathrm{GP}(n,k)\) through Chebyshev polynomials
• Critical groups of iterated cones
• The homology characters of the cyclic coverings of the knots of genus one
• The Arithmetical Theory of Linear Recurring Series
• Homology of Abelian Coverings of Links and Spatial Graphs
• A short proof of a theorem of Plans on the homology of the branched cyclic coverings of a knot

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