The relative fixity of a permutation group is the maximum proportion of the points fixed by a non-trivial element of the group, and the relative fixity of a graph is the relative fixity of its automorphism group, viewed as a permutation group on the vertex-set of the graph. We prove in this paper that the relative fixity of connected 2-arc-transitive graphs of a fixed valence tends to 0 as the number of vertices grows to infinity. We prove the same result for the class of arc-transitive graphs of a fixed prime valence, and more generally, for any class of arc-transitive locally-L graphs, where L is a fixed quasiprimitive graph-restrictive permutation group.

Lehner, F., Potocnik, P., Spiga, P. (2021). On fixity of arc-transitive graphs. SCIENCE CHINA. MATHEMATICS, 64(12), 2603-2610 [10.1007/s11425-020-1825-1].

On fixity of arc-transitive graphs

Spiga P.
2021

Abstract

The relative fixity of a permutation group is the maximum proportion of the points fixed by a non-trivial element of the group, and the relative fixity of a graph is the relative fixity of its automorphism group, viewed as a permutation group on the vertex-set of the graph. We prove in this paper that the relative fixity of connected 2-arc-transitive graphs of a fixed valence tends to 0 as the number of vertices grows to infinity. We prove the same result for the class of arc-transitive graphs of a fixed prime valence, and more generally, for any class of arc-transitive locally-L graphs, where L is a fixed quasiprimitive graph-restrictive permutation group.
Articolo in rivista - Articolo scientifico
20B25; arc-transitive; automorphism group; fixed points; fixity; graph; minimal degree; permutation group; vertex-transitive;
English
2021
64
12
2603
2610
open
Lehner, F., Potocnik, P., Spiga, P. (2021). On fixity of arc-transitive graphs. SCIENCE CHINA. MATHEMATICS, 64(12), 2603-2610 [10.1007/s11425-020-1825-1].
File in questo prodotto:
File Dimensione Formato  
Spiga-2021-Sci China Math-preprint.pdf

accesso aperto

Descrizione: Article
Tipologia di allegato: Submitted Version (Pre-print)
Licenza: Creative Commons
Dimensione 172.53 kB
Formato Adobe PDF
172.53 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/415913
Citazioni
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 1
Social impact