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The Jacobian of a graph and graph automorphisms. / Estélyi, István; Karabáš, Ján; Mednykh, Alexander и др.

в: Discrete Mathematics, Том 348, № 2, 114259, 02.02.2025.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Estélyi, I, Karabáš, J, Mednykh, A & Nedela, R 2025, 'The Jacobian of a graph and graph automorphisms', Discrete Mathematics, Том. 348, № 2, 114259. https://doi.org/10.1016/j.disc.2024.114259

APA

Estélyi, I., Karabáš, J., Mednykh, A., & Nedela, R. (2025). The Jacobian of a graph and graph automorphisms. Discrete Mathematics, 348(2), [114259]. https://doi.org/10.1016/j.disc.2024.114259

Vancouver

Estélyi I, Karabáš J, Mednykh A, Nedela R. The Jacobian of a graph and graph automorphisms. Discrete Mathematics. 2025 февр. 2;348(2):114259. doi: 10.1016/j.disc.2024.114259

Author

Estélyi, István ; Karabáš, Ján ; Mednykh, Alexander и др. / The Jacobian of a graph and graph automorphisms. в: Discrete Mathematics. 2025 ; Том 348, № 2.

BibTeX

@article{661620c85b02468094222b973cef8dec,
title = "The Jacobian of a graph and graph automorphisms",
abstract = "In the present paper we investigate the faithfulness of certain linear representations of groups of automorphisms of a graph X in the group of symmetries of the Jacobian of X. As a consequence we show that if a 3-edge-connected graph X admits a nonabelian semiregular group of automorphisms, then the Jacobian of X cannot be cyclic. In particular, Cayley graphs of degree at least three arising from nonabelian groups have non-cyclic Jacobians. While the size of the Jacobian of X is well-understood – it is equal to the number of spanning trees of X – the combinatorial interpretation of the rank of Jacobian of a graph is unknown. Our paper presents a contribution in this direction.",
keywords = "Automorphism, Flow, Graph, Jacobian",
author = "Istv{\'a}n Est{\'e}lyi and J{\'a}n Karab{\'a}{\v s} and Alexander Mednykh and Roman Nedela",
note = "Финансирующий спонсор Номер финансирования Акроним Ministry of Education and Science of the Russian Federation Minobrnauka Agent{\'u}ra na Podporu V{\'y}skumu a V{\'y}voja VEGA 02/0078/20 APVV Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences FWNF-2022-0005 SIM, SB RAS ",
year = "2025",
month = feb,
day = "2",
doi = "10.1016/j.disc.2024.114259",
language = "English",
volume = "348",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "2",

}

RIS

TY - JOUR

T1 - The Jacobian of a graph and graph automorphisms

AU - Estélyi, István

AU - Karabáš, Ján

AU - Mednykh, Alexander

AU - Nedela, Roman

N1 - Финансирующий спонсор Номер финансирования Акроним Ministry of Education and Science of the Russian Federation Minobrnauka Agentúra na Podporu Výskumu a Vývoja VEGA 02/0078/20 APVV Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences FWNF-2022-0005 SIM, SB RAS

PY - 2025/2/2

Y1 - 2025/2/2

N2 - In the present paper we investigate the faithfulness of certain linear representations of groups of automorphisms of a graph X in the group of symmetries of the Jacobian of X. As a consequence we show that if a 3-edge-connected graph X admits a nonabelian semiregular group of automorphisms, then the Jacobian of X cannot be cyclic. In particular, Cayley graphs of degree at least three arising from nonabelian groups have non-cyclic Jacobians. While the size of the Jacobian of X is well-understood – it is equal to the number of spanning trees of X – the combinatorial interpretation of the rank of Jacobian of a graph is unknown. Our paper presents a contribution in this direction.

AB - In the present paper we investigate the faithfulness of certain linear representations of groups of automorphisms of a graph X in the group of symmetries of the Jacobian of X. As a consequence we show that if a 3-edge-connected graph X admits a nonabelian semiregular group of automorphisms, then the Jacobian of X cannot be cyclic. In particular, Cayley graphs of degree at least three arising from nonabelian groups have non-cyclic Jacobians. While the size of the Jacobian of X is well-understood – it is equal to the number of spanning trees of X – the combinatorial interpretation of the rank of Jacobian of a graph is unknown. Our paper presents a contribution in this direction.

KW - Automorphism

KW - Flow

KW - Graph

KW - Jacobian

UR - https://www.mendeley.com/catalogue/40f2d5f6-a901-3485-97d9-56ff47ea1fcd/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85203432938&origin=inward&txGid=bfc2dc68f1d574b90c2cea7680e650d0

U2 - 10.1016/j.disc.2024.114259

DO - 10.1016/j.disc.2024.114259

M3 - Article

VL - 348

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 2

M1 - 114259

ER -

ID: 62799665