Geodesic
Locally primitive normal Cayley graphs of metacyclic groups
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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A complete characterization of locally primitive normal Cayley graphs of metacyclic groups is given. Namely, let $\Gamma={\rm Cay}(G,S)$ be such a graph, where $G\cong{\Bbb Z}_m.{\Bbb Z}_n$ is a metacyclic group and $m=p_1^{r_1}p_2^{r_2}\cdots p_t^{r_t}$ such that $p_1 < p_2 < \dots < p_t$. It is proved that $G\cong D_{2m}$ is a dihedral group, and $val(\Gamma)=p$ is a prime such that $p|(p_1(p_1-1),p_2-1,\dots,p_t-1)$. Moreover, three types of graphs are constructed which exactly form the class of locally primitive normal Cayley graphs of metacyclic groups.
DOI : 10.37236/185
Classification : 05C25 
@article{10_37236_185,
     author = {Jiangmin Pan},
     title = {Locally primitive normal {Cayley} graphs of metacyclic groups},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/185},
     zbl = {1186.05068},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/185/}
}
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Jiangmin Pan. Locally primitive normal Cayley graphs of metacyclic groups. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/185

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