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This paper concerns all-to-all network routing on regular digraphs. Inprevious work we focused on efficient routing in highly symmetric digraphs withlow diameter for fixed degree. Here, we show that every connected regulardigraph has an all-to-all routing scheme and associated schedule with nowaiting. In fact, this routing scheme becomes more efficient as the diametergoes down with respect to the degree and number of vertices. Lastly, we examinethe simple scheduling algorithm called ``farthest-distance-first'' and provethat it yields optimal schedules for all-to-all communication in networks ofinterest, including Kautz graphs.

Network Routing on Regular Digraphs and Their Line Graphs