Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree
Combinatorics
2025-03-28 v2
Abstract
The motion of a graph is the minimum number of vertices that are moved by a non-trivial automorphism. Equivalently, it can be defined as the minimal degree of its automorphism group (as a permutation group on the vertices). In this paper we develop some results on permutation groups (primitive and imprimitive) with small minimal degree. As a consequence of such results we classify vertex-transitive graphs whose motion is or a prime number.
Cite
@article{arxiv.2405.10088,
title = {Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree},
author = {Antonio Montero and Primož Potočnik},
journal= {arXiv preprint arXiv:2405.10088},
year = {2025}
}