Some constructions of highly arc-transitive digraphs (Q653999)

The descendant set of a fixed vertex \(v\) in an infinite graph is defined as the set of vertices reachable by a directed path from \(v\). The authors construct infinite highly arc-transitive digraphs with finite out-valency and whose sets of descendants are digraphs which have a homomorphism onto a directed (rooted) tree. Some of these constructions are based on results of \textit{D. M. Evans} [Eur. J. Comb. 18, No. 3, 281--286 (1997; Zbl 0873.05050); Bull. Lond. Math. Soc. 33, No. 5, 583--590 (2001; Zbl 1029.20002)].