9 research outputs found
Algebraic degrees of -Cayley digraphs over abelian groups
A digraph is called an -Cayley digraph if its automorphism group has an
-orbit semiregular subgroup. We determine the splitting fields of -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
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