The Plans Theorem for Cones over Generalized $ I $-Graphs Full article
| Journal |
Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2026, Volume: 67, Number: 1, Pages: 99-109 Pages count : 11 DOI: 10.1134/s0037446626010106 | ||||
| Tags | circulant graph, Laplacian matrix, critical group, Plans theorem | ||||
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования РФ | FWNF-2026-0026 |
Abstract:
We consider a family of graphs generalizing the family of -graphs, which in turn includes generalized Petersen graphs and prismatic graphs. The paper is devoted to the study of the critical group of a graph that is a cone over a generalized -graph. The main result of the article is an analog of the Plans theorem (1953), which describes the first homology group of an -sheeted cyclic cover of the three-dimensional sphere branched over a knot. It asserts that this homology group is almost a direct sum of two copies of a certain abelian group. In this paper, analogous results are established for the structure of the critical group of the graphs under consideration.
Cite:
Mednykh I.A.
The Plans Theorem for Cones over Generalized $ I $-Graphs
Siberian Mathematical Journal. 2026. V.67. N1. P.99-109. DOI: 10.1134/s0037446626010106 OpenAlex
The Plans Theorem for Cones over Generalized $ I $-Graphs
Siberian Mathematical Journal. 2026. V.67. N1. P.99-109. DOI: 10.1134/s0037446626010106 OpenAlex
Original:
Медных И.А.
Теорема Планса для конусов над обобщенным I–Графом
Сибирский математический журнал. 2026. Т.67. №1. С.121-134. DOI: 10.33048/smzh.2026.67.110
Теорема Планса для конусов над обобщенным I–Графом
Сибирский математический журнал. 2026. Т.67. №1. С.121-134. DOI: 10.33048/smzh.2026.67.110
Dates:
| Submitted: | May 6, 2025 |
| Accepted: | Jun 20, 2025 |
| Published print: | Jan 29, 2026 |
| Published online: | Jan 29, 2026 |
Identifiers:
| OpenAlex: | W7126022608 |
Citing:
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