DIGRAPHS WITH TREE-LIKE DESCENDANT SETS
We give certain properties which are satisfied by the descendant set of a vertex in a primitive distance-transitive digraph of finite out-valency and provide a strong structure theory for di- graphs satisfying these properties. In particular, we show that there are only countably many possibilities for the isomorphism type of such a descendant set, thereby confirming a conjecture of the first Author. 2000 Mathematics Subject Classification: 05C20, 05C38, 20B07, 20B15.