Two-fold orbital digraphs and other constructions

Abstract

The developments of group theory, such as the classification of finite simple groups, stimulated recent developments in algebraic graph theory. One of the remarkable tasks accomplished is the determination of all vertex-transitive graphs or order equal to the product of two primes ( cf, [6], [13] and [12] ). The construction of orbital digraphs is one of the basic tools in the study of vertex-transitive digraphs. In principle, the group-theoretical method used to construct orbital digraphs may not only be used to generate all vertex-transitive digraphs (cf. [3] and [7] ), but also makes it clear whether these vertex-transitive digraphs are arc-transitive or not.