On tetravalent normal edge-transitive Cayley graphs on the modular group

Authors: HESAM SHARIFI, MOHAMMAD REZA DARAFSHEH

Abstract: A Cayley graph $\Gamma=Cay(G, S)$ on a group $G$ with respective toa subset $S\subseteq G$, $S=S^{-1}, 1\notın S$, is said to be normaledge-transitive if $N_{\mathbb{A}ut(\Gamma)}(\rho(G))$ is transitiveon edges of $\Gamma$, where $\rho(G)$ is a subgroup of $\mathbb{A}ut(\Gamma)$isomorphic to $G$. We determine all connected tetravalent normaledge-transitive Cayley graphs on the modular group of order $8n$in the case that every element of $S$ is of order $4n$.

Keywords: Cayley graph, edge-transitive, modular group,

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