Infinite highly arc transitive digraphs and universal covering digraphs

A digraph (that is a directed graph) is said to be highly arc transitive if its automorphism group is transitive on the set of s-arcs for each s≥0. Several new constructions are given of infinite highly arc transitive digraphs. In particular, for Δ a connected, 1-arc transitive, bipartite digraph, a highly arc transitive digraph DL(Δ) is constructed and is shown to be a covering digraph for every digraph in a certain class D(Δ) of connected digraphs. Moreover, if Δ is locally finite, then DL(Δ) is a universal covering digraph for D(Δ). Further constructions of infinite highly arc transitive digraphs are given.