Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups
Algebra and discrete mathematics, Tome 13 (2012) no. 1, pp. 52-58
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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.
@article{ADM_2012_13_1_a5,
author = {Mohsen Ghasemi},
title = {Automorphism groups of tetravalent {Cayley} graphs on minimal non-abelian groups},
journal = {Algebra and discrete mathematics},
pages = {52--58},
publisher = {mathdoc},
volume = {13},
number = {1},
year = {2012},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ADM_2012_13_1_a5/}
}
Mohsen Ghasemi. Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups. Algebra and discrete mathematics, Tome 13 (2012) no. 1, pp. 52-58. http://geodesic.mathdoc.fr/item/ADM_2012_13_1_a5/