A classification of tetravalent edge-transitive metacirculants of odd order

In this paper a classification of tetravalent edge-transitive metacirculants is given. It is shown that a tetravalent edge-transitive metacirculant $Γ$ is a normal graph except for four known graphs. If further, $Γ$ is a Cayley graph of a non-abelian metacyclic group, then $Γ$ is half-transitive.

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