Characterising CCA Sylow cyclic groups whose order is not divisible by four

Luke Morgan, Joy Morris, Gabriel Verret

Abstract


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.


Keywords


CCA problem, Cayley graphs, edge-colouring, Sylow cyclic groups

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ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications