Arc-transitive bidihedrants

A permutation group on a set is said to be bi-regular if it is semiregular and has two orbits. In this paper, we give a classification of quasiprimitive permutation groups with a bi-regular dihedral subgroup. As applications, we characterize the family of arc-transitive graphs whose automorphism groups contain a bi-regular dihedral subgroup.We also find some new families of graphs as examples.