Given a connected finite graph Γ and a group G acting transitively on the vertices of Γ, we prove that the number of vertices of Γ and the order of G are bounded above by a function depending only on the valency of Γ and on the exponent of G. We also prove that the number of generators of a group G acting transitively on the arcs of a locally finite graph Γ cannot be bounded by a function of the valency alone.
Barbieri, M., Spiga, P. (2024). On the number of generators of groups acting arc-transitively on graphs. THE AUSTRALASIAN JOURNAL OF COMBINATORICS, 90(2), 187-198.
On the number of generators of groups acting arc-transitively on graphs
Spiga P.
2024
Abstract
Given a connected finite graph Γ and a group G acting transitively on the vertices of Γ, we prove that the number of vertices of Γ and the order of G are bounded above by a function depending only on the valency of Γ and on the exponent of G. We also prove that the number of generators of a group G acting transitively on the arcs of a locally finite graph Γ cannot be bounded by a function of the valency alone.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
Barbieri-2024-Australasian J Combinatorics-VoR.pdf
accesso aperto
Tipologia di allegato:
Publisher’s Version (Version of Record, VoR)
Licenza:
Creative Commons
Dimensione
147.83 kB
Formato
Adobe PDF
|
147.83 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
