On a representation of the automorphism group of a graph in a unimodular group | Sciact - Система учета научной деятельности ИМ СО РАН

On a representation of the automorphism group of a graph in a unimodular group Научная публикация

Журнал

Discrete Mathematics
ISSN: 0012-365X , E-ISSN: 1872-681X

Вых. Данные

Год: 2021, Том: 344, Номер: 12, Номер статьи : 112606, Страниц : DOI: 10.1016/j.disc.2021.112606

Ключевые слова

Automorphism; Graph; Unimodular matrix

Авторы

Estélyi I. ^1,2 , Karabáš J. ^1,3 , Nedela R. ^4,5 , Mednykh A. ^6,7

Организации

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

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.

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

Web of science:	WOS:000712876500025
Scopus:	2-s2.0-85114015564
OpenAlex:	W3196499653

БД	Цитирований
Scopus	2
OpenAlex	2
Web of science	1