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 $\Gamma$ is a normal graph except for four known graphs. If further, $\Gamma$ is a Cayley graph of a non-abelian metacyclic group, then $\Gamma$ is half-transitive. 
Shu Jiao Song
math.CO