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The Plans Theorem for Cones over Generalized -Graphs. / Mednykh, I. A.

In: Siberian Mathematical Journal, Vol. 67, No. 1, 01.2026, p. 99-109.

Research output: Contribution to journal › Article › peer-review

Harvard

Mednykh, IA 2026, 'The Plans Theorem for Cones over Generalized -Graphs', Siberian Mathematical Journal, vol. 67, no. 1, pp. 99-109. https://doi.org/10.1134/S0037446626010106

APA

Mednykh, I. A. (2026). The Plans Theorem for Cones over Generalized -Graphs. Siberian Mathematical Journal, 67(1), 99-109. https://doi.org/10.1134/S0037446626010106

Vancouver

Mednykh IA. The Plans Theorem for Cones over Generalized -Graphs. Siberian Mathematical Journal. 2026 Jan;67(1):99-109. doi: 10.1134/S0037446626010106

Author

Mednykh, I. A. / The Plans Theorem for Cones over Generalized -Graphs. In: Siberian Mathematical Journal. 2026 ; Vol. 67, No. 1. pp. 99-109.

BibTeX

@article{41536725660442caa668fe58d8acbfab,
title = "The Plans Theorem for Cones over Generalized -Graphs",
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.",
keywords = "517.545+519.173+519.177, Laplacian matrix, Plans theorem, circulant graph, critical group",
author = "Mednykh, {I. A.}",
note = "Mednykh, I.A. The Plans Theorem for Cones over Generalized I-Graphs. Sib Math J 67, 99–109 (2026). https://doi.org/10.1134/S0037446626010106 The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2026–0026).",
year = "2026",
month = jan,
doi = "10.1134/S0037446626010106",
language = "English",
volume = "67",
pages = "99--109",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "Pleiades Publishing",
number = "1",

}

RIS

TY - JOUR

T1 - The Plans Theorem for Cones over Generalized -Graphs

AU - Mednykh, I. A.

N1 - Mednykh, I.A. The Plans Theorem for Cones over Generalized I-Graphs. Sib Math J 67, 99–109 (2026). https://doi.org/10.1134/S0037446626010106 The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2026–0026).

PY - 2026/1

Y1 - 2026/1

N2 - 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.

AB - 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.

KW - 517.545+519.173+519.177

KW - Laplacian matrix

KW - Plans theorem

KW - circulant graph

KW - critical group

UR - https://www.scopus.com/pages/publications/105028605153

UR - https://www.mendeley.com/catalogue/503e9255-0353-33ca-8816-dd1516867c4b/

U2 - 10.1134/S0037446626010106

DO - 10.1134/S0037446626010106

M3 - Article

VL - 67

SP - 99

EP - 109

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 1

ER -

ID: 74322894