On the construction of radially Moore digraphs

A digraph with maximum out-degree d and radius k has at most 1+d+ · · ·+d vertices, as the Moore bound states. Regular digraphs attaining such a bound and whose diameter is at most k + 1 are called radially Moore digraphs. Knor [4] proved that these extremal digraphs do exist for any value of d ≥ 1 and k ≥ 1. In this paper, we introduce a digraph operator, based on the line digraph, which allow us to construct new radially Moore digraphs and recover the known ones. Besides, we show that for k = 2 a radially Moore digraph with as many central vertices as the degree do exist.