Cayley graphs on abelian groups

Abstract

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 $\mathrm{Aut}(\Gamma )=A⋊⟨i⟩$. 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.

References in corpus (3)

• Asymptotic enumeration of vertex-transitive graphs of fixed valency
• Automorphisms of Cayley graphs on generalised dicyclic groups
• Abelian Carter subgroups in finite permutation groups

Cited by in corpus (2)

• Automorphisms of Cayley graphs on generalised dicyclic groups
• Abelian Carter subgroups in finite permutation groups