Asymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power order

Abstract

We show that almost every Cayley graph Γ of an abelian group G of odd prime-power order has automorphism group as small as possible. Additionally, we show that almost every Cayley (di)graph Γ of an abelian group G of odd prime-power order that does not have automorphism group as small as possible is a normal Cayley (di)graph of G (that is, G L is normal in Aut(Γ)).