9 research outputs found

    Algebraic degrees of nn-Cayley digraphs over abelian groups

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    A digraph is called an nn-Cayley digraph if its automorphism group has an nn-orbit semiregular subgroup. We determine the splitting fields of nn-Cayley digraphs over abelian groups and compute a bound on their algebraic degrees, before applying our results on Cayley digraphs over non-abelian groups

    Semiregular automorphisms of cubic vertex-transitive graphs and the abelian normal quotient method

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    Sherpa Romeo green journal. Open accessWe characterise connected cubic graphs admitting a vertex-transitive group of automorphisms with an abelian normal subgroup that is not semiregular. We illustrate the utility of this result by using it to prove that the order of a semiregular subgroup of maximum order in a vertex-transitive group of automorphisms of a connected cubic graph grows with the order of the graph.Ye

    Arc-transitive graphs of valency 8 have a semiregular automorphism

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