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The Plans Theorem for Cones over Generalized $ I $-Graphs Full article

Journal Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260
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
Authors Mednykh I.A. 1,2
Affiliations
1 Novosibirsk State University, Novosibirsk, Russia
2 Sobolev Institute of Mathematics, Novosibirsk, Russia

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
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
Dates:
Submitted: May 6, 2025
Accepted: Jun 20, 2025
Published print: Jan 29, 2026
Published online: Jan 29, 2026
Identifiers:
OpenAlex: W7126022608
Citing: Пока нет цитирований
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