A classification of cubic bicirculants

The well-known Petersen graph G(5,2)G(5,2) admits a semi-regular automorphism αα acting on the vertex set with two orbits of equal size. This makes it a bicirculant. It is shown that trivalent bicirculants fall into four classes. Some basic properties of trivalent bicirculants are explored and the connection to combinatorial and geometric configurations are studied. Some analogues of the polycirculant conjecture are mentioned.