Two Results Concerning Distance-Regular Directed Graphs


D. Combe and D. E. Taylor


Research Report 99-13
Date: 10 June 1999


The study of distance-regular directed graphs can be reduced to that of short distance-regular directed graphs. We consider the eigenspaces of the intersection matrix of a short distance-regular directed graph and show that nearly all the eigenvalues are nonreal. Next we show that a nontrivial short distance-regular directed graph is primitive.

Key phrases

distance-regular graph. distance-transitive graph. directed graph. primitivity. adjacency algebra.

AMS Subject Classification (1991)

Primary: 05C20
Secondary: 05C25, 05E30


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