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Abstract

Abstract. The automorphism groups Aut(C(G, X ))and Aut (CM(G, X, p)) of a Cayley graph C(G, X ) and a Cayley map CM (G, X, p) both contain an isomorphic copy of the underlying group G acting via left translations. In our paper, we show that both automorphism groups are rotary extensions of the group G by the stabilizer subgroup of the vertex 1 G . We use this description to derive necessary and sufficient conditions to be satisfied by a finite group in order to be the (full) automorphism group of a Cayley graph or map and classify all the finite groups that can be represented as the (full) automorphism group of some Cayley graph or map.

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“…As far as we are aware, this definition was coined by Robert Jajcay in [5]. Theorem 7 in [5] shows that each finite group not isomorphic to Z 3 or Z 2 2 possesses an MRR.…”

“…As far as we are aware, this definition was coined by Robert Jajcay in [5]. Theorem 7 in [5] shows that each finite group not isomorphic to Z 3 or Z 2 2 possesses an MRR. Observe that CM (R, S, r) is a MRR if and only if the only automorphism of CM (R, S, r) fixing a vertex is the identity.…”