ABSTRACT
Important in the study of t-wise balanced designs is the classification of designs that have a given automorphism group, family of automorphism groups or type of automorphism. This chapter considers designs whose points are the edges of a graph G that have AUT(G) as an automorphism group. A graphical design is a proper t-wise balanced design with parameters that has the symmetric group as an automorphism group. It is now not difficult to see that every subgraph in the orbit can be completed to a subgraph in the orbit of in exactly one way and similarly every subgraph in the orbit of is contained in exactly two subgraphs in the orbit.
