  Let $A$ be an abelian group and let $\iota$ be the automorphism of $A$
defined by $i:a\mapsto a^{-1}$. A Cayley graph $\Gamma=\mathrm{Cay}(A,S)$ is
said to have an automorphism group \emph{as small as possible} if
$\mathrm{Aut}(\Gamma)= A\rtimes\langle i\rangle$. In this paper, we show that
almost all Cayley graphs on abelian groups have automorphism group as small as
possible, proving a conjecture of Babai and Godsil.
