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Frelih, Boštjan; Kovács, István; Kutnar, Klavdija
Journal of algebraic combinatorics, 06/2022, Volume: 55, Issue: 4Journal Article
A finite simple graph is called a k -multicirculant if its automorphism group contains a cyclic semiregular subgroup having k orbits on the vertex set. It was shown by Giudici et al. that, if k is squarefree and coprime to 6, then a cubic arc-transitive k -multicirculant has at most 6 k 2 vertices (J. Combin. Theory Ser. B, 2017). In this paper, we classify the latter graphs under the assumption that their semiregular cyclic subgroups are contained in a soluble group of automorphisms acting transitively on the arc set of the graphs. As an application, cubic arc-transitive p -multicirculants are completely described for each odd prime p .
