On Color Preserving Automorphisms of Cayley Graphs of Odd Square-free Order Edward Dobson
نویسندگان
چکیده
An automorphism α of a Cayley graph Cay(G,S) of a group G with connection set S is color-preserving if α(g, gs) = (h, hs) or (h, hs−1) for every edge (g, gs) ∈ E(Cay(G,S)). If every color-preserving automorphism of Cay(G,S) is also affine, then Cay(G,S) is a CCA (Cayley color automorphism) graph. If every Cayley graph Cay(G,S) is a CCA graph, then G is a CCA group. Hujdurović, Kutnar, D.W. Morris, and J. Morris have shown that every non-CCA group G contains a section isomorphic to the nonabelian group F21 of order 21. We first show that there is a unique non-CCA Cayley graph Γ of F21. We then show that if Cay(G,S) is a non-CCA graph of a group G of odd square-free order, then G = H×F21 for some CCA group H, and Cay(G,S) = Cay(H,T ) Γ.
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