Distance-transitive Seymour-tight orientation conjecture

A Seymour-tight orientation is an orientation $G$ in which every vertex $v$ satisfies $|N^+_2(G,v)|=|N^+_1(G,v)|$. A digraph is distance-transitive when its automorphism group is transitive on ordered pairs of vertices at each fixed directed distance.

Distance-transitive Seymour-tightness conjecture. Every distance-transitive digraph is a Seymour-tight orientation.

Directed cycles, Paley tournaments, and certain lexicographic products provide known distance-transitive Seymour-tight examples. The proposed conjecture seeks a complete structural property for all distance-transitive digraphs and remains open.