Distance transitive digraphs

✍ Scribed by Clement W.H. Lam

• Publisher: Elsevier Science
• Year: 1980
• Tongue: English
• Weight: 980 KB
• Volume: 29
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(80)90155-7

✦ Synopsis

A 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 w of the digraph such that T(U) = x and T(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. Th ere are 28 possibilities and each can be realized by the constructions of Section 2.