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

This article is cited in 2 scientific papers (total in 2 papers)

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
Received: 13.10.2011
Revised: 27.11.2011
Language:

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}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ghasemi M., “A Classification of Tetravalent One-Regular Graphs of Order 3P(2)”, Colloq. Math., 128:1 (2012), 15–24  crossref  mathscinet  zmath  isi  scopus
    2. Ghasemi M., “An Algorithmic-Type Classification of Tetravalent One-Regular Graphs Using Computer Algebra Tools”, Fundam. Inform., 135:3 (2014), 211–228  crossref  mathscinet  zmath  isi  scopus
  • Algebra and Discrete Mathematics
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