Automorphisms of Cayley graphs (Q1187136)

Let \(A(\Gamma)\) denote the automorphism group of a Cayley graph \(\Gamma\) of a group \(S\), and let \(N(S)\) denote the normalizer of \(S\) in the symmetric group on the vertex set (which is identified with \(S)\) of \(\Gamma\). The action of \(A(\Gamma)\cap N(S)\) on various partitions of the edge-set of \(\Gamma\) is carefully studied.