Some Normal Edge-transitive Cayley Graphs on Dihedral Groups

Volume 2, Issue 3, pp 448--452
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Authors

A. Asghar Talebi - Department of Mathematics University of Mazandaran, Babolsar, Iran

Abstract

Let $G$ be a group and $S$ a subset of $G$ such that $1_G\not\in S$ and $S=S−1$. Let $\Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to. Then $\Gamma$ is said to be normal edge-transitive, if $N_{Aut}(\Gamma)(G)$ acts transitively on edges. In this paper we determine all normal edge-transitive Cayley graphs on a dihedral Group $D_{2n}$ of valency $n$. In addition we classify normal edge-transitive Cayley graphs $\Gamma=Cay(D_{2p},S)$ of valency four, for a prime $p$ and give some normal edge-transitive Cayley graphs $\Gamma=Cay(D_{2n},S)$ of valency four that $n$ is not a prime .

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ISRP Style

A. Asghar Talebi, Some Normal Edge-transitive Cayley Graphs on Dihedral Groups, Journal of Mathematics and Computer Science, 2 (2011), no. 3, 448--452

AMA Style

Talebi A. Asghar, Some Normal Edge-transitive Cayley Graphs on Dihedral Groups. J Math Comput SCI-JM. (2011); 2(3):448--452

Chicago/Turabian Style

Talebi, A. Asghar. "Some Normal Edge-transitive Cayley Graphs on Dihedral Groups." Journal of Mathematics and Computer Science, 2, no. 3 (2011): 448--452

Keywords

• Cayley graph
• normal edge-transitive
• Dihedral groups

•  20B15
•  05C25
•  05E18

References

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