# Two Results Concerning Distance-Regular Directed Graphs

## Author

**D. Combe** and **D. E. Taylor**

## Status

Research Report 99-13

Date: 10 June 1999

## Abstract

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

## Content

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Sydney Mathematics and Statistics