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On the jacobian group of a cone over a circulant graph. / Grunwald, L. A.; Mednykh, I. A.

In: Mathematical Notes of NEFU, Vol. 28, No. 2, 6, 03.2021, p. 88-101.

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

Harvard

Grunwald, LA & Mednykh, IA 2021, 'On the jacobian group of a cone over a circulant graph', Mathematical Notes of NEFU, vol. 28, no. 2, 6, pp. 88-101. https://doi.org/10.25587/SVFU.2021.32.84.006

APA

Grunwald, L. A., & Mednykh, I. A. (2021). On the jacobian group of a cone over a circulant graph. Mathematical Notes of NEFU, 28(2), 88-101. [6]. https://doi.org/10.25587/SVFU.2021.32.84.006

Vancouver

Grunwald LA, Mednykh IA. On the jacobian group of a cone over a circulant graph. Mathematical Notes of NEFU. 2021 Mar;28(2):88-101. 6. doi: 10.25587/SVFU.2021.32.84.006

Author

Grunwald, L. A. ; Mednykh, I. A. / On the jacobian group of a cone over a circulant graph. In: Mathematical Notes of NEFU. 2021 ; Vol. 28, No. 2. pp. 88-101.

BibTeX

@article{97ad31303ba74587ad63cdc562baaea1,
title = "On the jacobian group of a cone over a circulant graph",
abstract = "For any given graph G, consider the graph Ĝ which is a cone over G. We study two important invariants of such a cone, namely, the complexity (the number of spanning trees) and the Jacobian of the graph. We prove that complexity of graph Ĝ coincides with the number of rooted spanning forests in G and the Jacobian of Ĝ is isomorphic to the cokernel of the operator I + L(G), where L(G) is the Laplacian of G and I is the identity matrix. As a consequence, one can calculate the complexity of Ĝ as det(I + L(G)). As an application, we establish general structural theorems for the Jacobian of Ĝ in the case when G is a circulant graph or cobordism of two circulant graphs.",
keywords = "Chebyshev polynomial, Circulant graph, Cone over graph, Laplacian matrix, Spanning forest, Spanning tree",
author = "Grunwald, {L. A.} and Mednykh, {I. A.}",
note = "Funding Information: The study of the second named author was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. 0314-2019-0007). Publisher Copyright: {\textcopyright} 2021 L. A. Grunwald and I. A. Mednykh.",
year = "2021",
month = mar,
doi = "10.25587/SVFU.2021.32.84.006",
language = "English",
volume = "28",
pages = "88--101",
journal = "Математические заметки СВФУ",
issn = "2411-9326",
publisher = "M. K. Ammosov North-Eastern Federal University",
number = "2",

}

RIS

TY - JOUR

T1 - On the jacobian group of a cone over a circulant graph

AU - Grunwald, L. A.

AU - Mednykh, I. A.

N1 - Funding Information: The study of the second named author was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. 0314-2019-0007). Publisher Copyright: © 2021 L. A. Grunwald and I. A. Mednykh.

PY - 2021/3

Y1 - 2021/3

N2 - For any given graph G, consider the graph Ĝ which is a cone over G. We study two important invariants of such a cone, namely, the complexity (the number of spanning trees) and the Jacobian of the graph. We prove that complexity of graph Ĝ coincides with the number of rooted spanning forests in G and the Jacobian of Ĝ is isomorphic to the cokernel of the operator I + L(G), where L(G) is the Laplacian of G and I is the identity matrix. As a consequence, one can calculate the complexity of Ĝ as det(I + L(G)). As an application, we establish general structural theorems for the Jacobian of Ĝ in the case when G is a circulant graph or cobordism of two circulant graphs.

AB - For any given graph G, consider the graph Ĝ which is a cone over G. We study two important invariants of such a cone, namely, the complexity (the number of spanning trees) and the Jacobian of the graph. We prove that complexity of graph Ĝ coincides with the number of rooted spanning forests in G and the Jacobian of Ĝ is isomorphic to the cokernel of the operator I + L(G), where L(G) is the Laplacian of G and I is the identity matrix. As a consequence, one can calculate the complexity of Ĝ as det(I + L(G)). As an application, we establish general structural theorems for the Jacobian of Ĝ in the case when G is a circulant graph or cobordism of two circulant graphs.

KW - Chebyshev polynomial

KW - Circulant graph

KW - Cone over graph

KW - Laplacian matrix

KW - Spanning forest

KW - Spanning tree

UR - http://www.scopus.com/inward/record.url?scp=85112403009&partnerID=8YFLogxK

UR - https://elibrary.ru/item.asp?id=46343993

U2 - 10.25587/SVFU.2021.32.84.006

DO - 10.25587/SVFU.2021.32.84.006

M3 - Article

AN - SCOPUS:85112403009

VL - 28

SP - 88

EP - 101

JO - Математические заметки СВФУ

JF - Математические заметки СВФУ

SN - 2411-9326

IS - 2

M1 - 6

ER -

ID: 34097112