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arXiv · 2005.11983

On fixity of arc-transitive graphs

Florian Lehner·Primoz Potocnik·Pablo Spiga
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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.

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Florian Lehner, Primoz Potocnik, Pablo Spiga. 2020-05-25. On fixity of arc-transitive graphs. https://arxiv.org/abs/2005.11983

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