Morris, Joy

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Characterising CCA Sylow cyclic groups whose order is not divisible by four
(Drustvo Matematikov, Fizikov in Astronomov, 2018) Morgan, Luke; Morris, Joy; Verret, Gabriel
A Cayley graph on a group G has a natural edge-colouring. We say that such a graph is CCA if every automorphism of the graph that preserves this edge-colouring is an element of the normaliser of the regular representation of G. A group G is then said to be CCA if every connected Cayley graph on G is CCA. Our main result is a characterisation of non-CCA graphs on groups that are Sylow cyclic and whose order is not divisible by four. We also provide several new constructions of non-CCA graphs.
Semiregular automorphisms of cubic vertex-transitive graphs and the abelian normal quotient method
(Electronic Journal of Combinatorics, 2015) Morris, Joy; Spiga, Pablo; Verret, Gabriel
We 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.