Distance transitive digraphs

AbstractA digraph is said to be distance-transitive if for all vertices u, v, x, y such that d(u, v) = d(x, y) there is an automorphism π of the digraph such that π(u) = x and π(v) = y. Some examples of distance-transitive digraphs are given in Section 2. Section 3 defines the intersection matrix and gives some of its properties. Section 4 proves that every distance-transitive digraph with diameter 2 is a balanced incomplete block design with the Hadamard parameters. Intersection matrices of distance-transitive digraphs with diameter 3 and valency not larger than 20 are generated. There are 28 possibilities and each can be realized by the constructions of Section 2