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.
Highlights
All groups and all graphs in this paper are finite
We obtain a characterisation of non-CCA groups whose order is not divisible by four, in which every Sylow subgroup is cyclic. This generalises the work of [3], which dealt with the case of groups of odd squarefree order
Let A be a colour-preserving group of automorphisms of Cay(G, S), let N be a normal subgroup of A and let K be the kernel of the action of A on the N -orbits
Summary
All groups and all graphs in this paper are finite. Let G be a group and let S be an inverseclosed subset of G. Its group of colour-preserving automorphisms is denoted Autc(Cay(G, S)). The Cayley graph Cay(G, S) is CCA (Cayley colour automorphism) if Autc(Cay(G, S)) = GR Aut±1(G, S). This generalises results from [5]. This generalises the work of [3], which dealt with the case of groups of odd squarefree order
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