Edge‐transitive cubic graphs of twice square‐free order

Abstract A graph is edge‐transitive if its automorphism group acts transitively on the edge set. This paper presents a complete classification for connected edge‐transitive cubic graphs of order , where is even and square‐free. In particular, it is shown that such a graph is either symmetric or isomorphic to one of the following graphs: a semisymmetric graph of order 420, a semisymmetric graph of order 29,260, and five families of semisymmetric graphs constructed from the simple group .