Cayley graphs on abelian groups

2013/06/17 by Dobson, Edward, Spiga, Pablo, Verret, Gabriel
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1306.3747

Abstract

Let A be an abelian group and let ι be the automorphism of A defined by i:a↦ a^-1. A Cayley graph Γ=Cay(A,S) is said to have an automorphism group as small as possible if Aut(Γ)= A\rtimes⟨ 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.

Related

• On the existence and the enumeration of bipartite regular representations of Cayley graphs over abelian groups
• On The automorphism groups of us-Cayley graphs
• Automorphism groups of graphs
• Cayley graphs of more than one abelian group
• On automorphisms and structural properties of generalized Cayley graphs