On the action of non-Abelian groups on graphs

AbstractFinite groups may be classified as to whether or not they have regular representations as automorphism groups of graphs. Such a classification is begun here for non-Abelian groups (classification of Abelian groups being already in the literature) with a classification of the dihedral groups, the groups of order p3 for p an odd prime (except for one group of order 27), and the generalized dicyclic groups. It is further shown that the class of groups (other than C2) having the above regular representations is closed under the operation of direct product