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On a representation of the automorphism group of a graph in a unimodular group Full article

Journal Discrete Mathematics
ISSN: 0012-365X , E-ISSN: 1872-681X
Output data Year: 2021, Volume: 344, Number: 12, Article number : 112606, Pages count : DOI: 10.1016/j.disc.2021.112606
Tags Automorphism; Graph; Unimodular matrix
Authors Estélyi I. 1,2 , Karabáš J. 1,3 , Nedela R. 4,5 , Mednykh A. 6,7
Affiliations
1 NTIS, University of West Bohemia, Technická 8, Plzeň 330100, Czech Republic
2 Faculty of Information Technology, University of Pannonia, Egyetem u. 10, Veszprém, 8200, Hungary
3 Faculty of Natural Sciences, Matej Bel University, Tajovského 40, Banská Bystrica, 97401, Slovakia
4 Faculty of Applied Sciences, University of West Bohemia, Technická 8, Plzeň 330100, Czech Republic
5 Mathematical Institute, Slovak Academy of Sciences, Ďumbierska 1, Banská Bystrica, 97411, Slovakia
6 Sobolev Institute of Mathematics, Pr. Koptyuga 4, Novosibirsk, 630090, Russian Federation
7 Novosibirsk State University, Pirogova 2, Novosibirsk, 630090, Russian Federation

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.
Cite: 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. V.344. N12. 112606 . DOI: 10.1016/j.disc.2021.112606 WOS Scopus OpenAlex
Identifiers:
Web of science: WOS:000712876500025
Scopus: 2-s2.0-85114015564
OpenAlex: W3196499653
Citing:
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Scopus 2
OpenAlex 2
Web of science 1
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