2020/05/25 by Lehner, Florian, Potocnik, Primoz, Spiga, Pablo · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2005.11983
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.