## 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.

Original language | English |
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Journal | Science China / Mathematics |

DOIs | |

Publication status | Accepted/In press - 2021 |

## Keywords

- 20B25
- arc-transitive
- automorphism group
- fixed points
- fixity
- graph
- minimal degree
- permutation group
- vertex-transitive

## ASJC Scopus subject areas

- Mathematics(all)