Asymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power order

Edward Dobson

Abstract


We show that almost every Cayley graph Γ of an abelian group G of odd prime-power order has automorphism group as small as possible.  Additionally, we show that almost every Cayley (di)graph Γ of an abelian group G of odd prime-power order that does not have automorphism group as small as possible is a normal Cayley (di)graph of G (that is, GL is normal in Aut(Γ)).

Keywords


Cayley graph, abelian group, automorphism group, asymptotic, p-group

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DOI: https://doi.org/10.26493/1855-3974.120.c55

ISSN: 1855-3974

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