Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree

 @Unpublished{MonteroPotocnik_VertexTransitiveGraphs_preprint,
    author = "Montero, Antonio and Potočnik, Primož",
    note = "In preparation",
    title = "Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree",
    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 $4$ or a prime number.",
    keywords = "Fixity, Motion, Minimal degree, Graphs, Permutation Groups, ",
    url = "https://arxiv.org/abs/2405.10088"
}