Finite vertex-biprimitive edge-transitive tetravalent graphs

Ivanov and Iofinova classified vertex-biprimitive edge-transitive cubic graphs in 1985. As a natural generalization of Ivanov and Iofinova’s work, in this paper we present a classification of tetravalent graphs which are GG-vertex-biprimitive and GG-edge-transitive for some automorphism group GG of the graphs.