On color-preserving automorphisms of Cayley graphs of odd square-free order

An automorphism of a Cayley graph of a group G with connection set S is color-preserving if or for every edge . If every color-preserving automorphism of is also affine, then is a Cayley color automorphism (CCA) graph. If every Cayley graph is a CCA graph, then G is a CCA group. HujduroviAc et al. have shown that every non-CCA group G contains a section isomorphic to the non-abelian group of order 21. We first show that there is a unique non-CCA Cayley graph of . We then show that if is a non-CCA graph of a group G of odd square-free order, then for some CCA group H, and .