Constructing continuum many countable, primitive, unbalanced digraphs

AbstractWe construct continuum many non-isomorphic countable digraphs which are highly arc transitive, have finite out-valency and infinite in-valency, and whose automorphism groups are primitive

Infinite primitive and distance transitive directed graphs of finite out-valency

We give certain properties which are satisfied by the descendant set of a vertex in an infinite, primitive, distance transitive digraph of finite out-valency and provide a strong structure theory for digraphs 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. As a partial converse, we show that certain related conditions on a countable digraph are sufficient for it to occur as the descendant set of a primitive, distance transitive digraph