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On a representation of the automorphism group of a graph in a unimodular group. / Estélyi, István; Karabáš, Ján; Nedela, Roman et al.

In: Discrete Mathematics, Vol. 344, No. 12, 112606, 12.2021.

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

Harvard

Estélyi, I, Karabáš, J, Nedela, R & Mednykh, A 2021, 'On a representation of the automorphism group of a graph in a unimodular group', Discrete Mathematics, vol. 344, no. 12, 112606. https://doi.org/10.1016/j.disc.2021.112606

APA

Estélyi, I., Karabáš, J., Nedela, R., & Mednykh, A. (2021). On a representation of the automorphism group of a graph in a unimodular group. Discrete Mathematics, 344(12), [112606]. https://doi.org/10.1016/j.disc.2021.112606

Vancouver

Estélyi I, Karabáš J, Nedela R, Mednykh A. On a representation of the automorphism group of a graph in a unimodular group. Discrete Mathematics. 2021 Dec;344(12):112606. doi: 10.1016/j.disc.2021.112606

Author

Estélyi, István ; Karabáš, Ján ; Nedela, Roman et al. / On a representation of the automorphism group of a graph in a unimodular group. In: Discrete Mathematics. 2021 ; Vol. 344, No. 12.

BibTeX

@article{d6c4ee9c475e4553956867ee6375341c,
title = "On a representation of the automorphism group of a graph in a unimodular group",
abstract = "We investigate a representation of the automorphism group of a connected graph X in the group of unimodular matrices Uβ of dimension β, where β is the Betti number of graph X. We classify the graphs for which the automorphism group does not embed into Uβ. It follows that if X has no pendant vertices and X is not a simple cycle, then the representation is faithful and AutX acts faithfully on H1(X,Z). The latter statement can be viewed as a discrete analogue of a classical Hurwitz's theorem on Riemann surfaces of genera greater than one.",
keywords = "Automorphism, Graph, Unimodular matrix",
author = "Istv{\'a}n Est{\'e}lyi and J{\'a}n Karab{\'a}{\v s} and Roman Nedela and Alexander Mednykh",
note = "Funding Information: The first three authors were supported by the grant GACR 20-15576S . The first author acknowledges the financial support of Sz{\'e}chenyi 2020 under the EFOP-3.6.1-16-2016-00015 grant. The second and third author were supported by the grant No. APVV-19-0308 of Slovak Research and Development Agency . The fourth author was supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation . Funding Information: The authors express thanks to the anonymous referee for his/her useful comments which helped a lot to improve the presentation. The first three authors were supported by the grant GACR 20-15576S. The first author acknowledges the financial support of Sz?chenyi 2020 under the EFOP-3.6.1-16-2016-00015 grant. The second and third author were supported by the grant No. APVV-19-0308 of Slovak Research and Development Agency. The fourth author was supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",
year = "2021",
month = dec,
doi = "10.1016/j.disc.2021.112606",
language = "English",
volume = "344",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "12",

}

RIS

TY - JOUR

T1 - On a representation of the automorphism group of a graph in a unimodular group

AU - Estélyi, István

AU - Karabáš, Ján

AU - Nedela, Roman

AU - Mednykh, Alexander

N1 - Funding Information: The first three authors were supported by the grant GACR 20-15576S . The first author acknowledges the financial support of Széchenyi 2020 under the EFOP-3.6.1-16-2016-00015 grant. The second and third author were supported by the grant No. APVV-19-0308 of Slovak Research and Development Agency . The fourth author was supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation . Funding Information: The authors express thanks to the anonymous referee for his/her useful comments which helped a lot to improve the presentation. The first three authors were supported by the grant GACR 20-15576S. The first author acknowledges the financial support of Sz?chenyi 2020 under the EFOP-3.6.1-16-2016-00015 grant. The second and third author were supported by the grant No. APVV-19-0308 of Slovak Research and Development Agency. The fourth author was supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: © 2021 Elsevier B.V.

PY - 2021/12

Y1 - 2021/12

N2 - We investigate a representation of the automorphism group of a connected graph X in the group of unimodular matrices Uβ of dimension β, where β is the Betti number of graph X. We classify the graphs for which the automorphism group does not embed into Uβ. It follows that if X has no pendant vertices and X is not a simple cycle, then the representation is faithful and AutX acts faithfully on H1(X,Z). The latter statement can be viewed as a discrete analogue of a classical Hurwitz's theorem on Riemann surfaces of genera greater than one.

AB - We investigate a representation of the automorphism group of a connected graph X in the group of unimodular matrices Uβ of dimension β, where β is the Betti number of graph X. We classify the graphs for which the automorphism group does not embed into Uβ. It follows that if X has no pendant vertices and X is not a simple cycle, then the representation is faithful and AutX acts faithfully on H1(X,Z). The latter statement can be viewed as a discrete analogue of a classical Hurwitz's theorem on Riemann surfaces of genera greater than one.

KW - Automorphism

KW - Graph

KW - Unimodular matrix

UR - http://www.scopus.com/inward/record.url?scp=85114015564&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2021.112606

DO - 10.1016/j.disc.2021.112606

M3 - Article

AN - SCOPUS:85114015564

VL - 344

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 12

M1 - 112606

ER -

ID: 34154673