Cayley graphs on abelian groups

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 sma...

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Bibliographic Details
Published inCombinatorica (Budapest. 1981) Vol. 36; no. 4; pp. 371 - 393
Main Authors Dobson, Edward, Spiga, Pablo, Verret, Gabriel
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2016
Springer Nature B.V
Subjects
Combinatorics
Graphs
Mathematics
Mathematics and Statistics
Original Paper
20B25
05E18
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Summary: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.
ISSN:0209-9683
1439-6912
DOI:10.1007/s00493-015-3136-5