On a representation of the automorphism group of a graph in a unimodular group
| dc.contributor.author | Estélyi, István | |
| dc.contributor.author | Karabáš, Ján | |
| dc.contributor.author | Nedela, Roman | |
| dc.contributor.author | Mednykh, Alexander | |
| dc.date.accessioned | 2021-12-06T11:00:26Z | |
| dc.date.available | 2021-12-06T11:00:26Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | V práci klasifikujeme souvislé grafy, kterých grupa automorfismů má věrnou reprezentaci v grupě unimodulárních matic dimenze b, kde b je Bettiho číslo grafu. Pokud stupeň každého vrchola je aspoň dva a graf není cyklus, pak je reprezentace věrná. Výsledek je možné považovat za analogii obdobného výsledku pro Riemannovy plochy rodu >1. | cs |
| dc.description.abstract-translated | We investigate a representation of the automorphism group of a connected graph X in the group of unimodular matrices U(b) of dimension b, where b is the Betti number of graph X. We classify the graphs for which the automorphism group does not embed into U(b) . It follows that if X has no pendant vertices and X is not a simple cycle, then the representation is faithful and Aut(X) acts faithfully on homology group H(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. | en |
| dc.format | 4 s. | cs |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | 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, roč. 344, č. 12, s. nestránkováno. ISSN: 0012-365X | cs |
| dc.identifier.document-number | 712876500025 | |
| dc.identifier.doi | 10.1016/j.disc.2021.112606 | |
| dc.identifier.issn | 0012-365X | |
| dc.identifier.obd | 43933835 | |
| dc.identifier.uri | 2-s2.0-85114015564 | |
| dc.identifier.uri | http://hdl.handle.net/11025/46282 | |
| dc.language.iso | en | en |
| dc.project.ID | GA20-15576S/Nakrytí grafů: Symetrie a složitost | cs |
| dc.publisher | Elsevier | en |
| dc.relation.ispartofseries | Discrete Mathematics | en |
| dc.rights | Plný text je přístupný v rámci univerzity přihlášeným uživatelům. | cs |
| dc.rights | © Elsevier | en |
| dc.rights.access | restrictedAccess | en |
| dc.subject | graf, automorfismus, unimodulární matice | cs |
| dc.subject.translated | graph | en |
| dc.subject.translated | automorphism | en |
| dc.subject.translated | unimodular matrix | en |
| dc.title | On a representation of the automorphism group of a graph in a unimodular group | en |
| dc.title.alternative | O reprezentaci grupy automorfismů grafů v unimodulární grupě | cs |
| dc.type | článek | cs |
| dc.type | article | en |
| dc.type.status | Peer-reviewed | en |
| dc.type.version | publishedVersion | en |