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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2012, Volume 13, Issue 1, Pages 52–58 (Mi adm65)

RESEARCH ARTICLE

Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups

Mohsen Ghasemi

Department of Mathematics, Urmia University, Urmia 57135, Iran

Abstract: A Cayley graph $X=\mathrm{Cay}(G,S)$ is called normal for $G$ if the right regular representation $R(G)$ of $G$ is normal in the full automorphism group $\mathrm{Aut}(X)$ of $X$. In the present paper it is proved that all connected tetravalent Cayley graphs on a minimal non-abelian group $G$ are normal when $(|G|, 2)=(|G|,3)=1$, and $X$ is not isomorphic to either Cay$(G,S)$, where $|G|=5^n$, and $|\mathrm{Aut}(X)|=2^m.3.5^n$, where $m \in \{2,3\}$ and $n\geq 3$, or Cay$(G,S)$ where $|G|=5q^n$ ($q$ is prime) and $|\mathrm{Aut}(X)|=2^m.3.5.q^n$, where $q\geq 7$, $m \in \{2,3\}$ and $n\geq 1$.

Keywords: Cayley graph, normal Cayley graph, minimal non-abelian group.

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Bibliographic databases:
MSC: 05C25, 20B25
Revised: 27.11.2011
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Citation: Mohsen Ghasemi, “Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups”, Algebra Discrete Math., 13:1 (2012), 52–58

Citation in format AMSBIB
\Bibitem{Gha12} \by Mohsen~Ghasemi \paper Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups \jour Algebra Discrete Math. \yr 2012 \vol 13 \issue 1 \pages 52--58 \mathnet{http://mi.mathnet.ru/adm65} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2963825} \zmath{https://zbmath.org/?q=an:1257.05058}