The Structure of Automorphism Groups of Cayley Graphs and Maps.

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. [ABSTRACT FROM AUTHOR]