Descendants in highly arc transitive digraphs Original Research Article

A digraph is said to be highly arc transitive if its automorphism group acts transitively on the set of s-arcs for all s⩾0. The set of descendants of a directed line is defined as the set of all vertices that can be reached by a directed path from some vertex in the line. The structure of the subdigraph in a locally finite highly arc transitive digraph spanned by the set of descendants of a line is described and this knowledge is used to answer a question of Cameron, Praeger and Wormald. In addition another question of Cameron, Praeger and Wormald is settled.