Abstract
LetX G,H denote the Cayley graph of a finite groupG with respect to a subsetH. It is well-known that its automorphism groupA(XG,H) must contain the regular subgroupL G corresponding to the set of left multiplications by elements ofG. This paper is concerned with minimizing the index [A(XG,H)∶LG] for givenG, in particular when this index is always greater than 1. IfG is abelian but not one of seven exceptional groups, then a Cayley graph ofG exists for which this index is at most 2. Nearly complete results for the generalized dicyclic groups are also obtained.
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Imrich, W., Watkins, M.E. On automorphism groups of Cayley graphs. Period Math Hung 7, 243–258 (1976). https://doi.org/10.1007/BF02017943
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DOI: https://doi.org/10.1007/BF02017943