Let A be an abelian group and let ι be the automorphism of A defined by: ι: 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⋊<ι>. 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.
Dobson, E., Spiga, P., Verret, G. (2016). Cayley graphs on abelian groups. COMBINATORICA, 36(4), 371-393 [10.1007/s00493-015-3136-5].
Cayley graphs on abelian groups
SPIGA, PABLOSecondo
;
2016
Abstract
Let A be an abelian group and let ι be the automorphism of A defined by: ι: 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⋊<ι>. 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.
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