A note on radially Moore digraphs

Let D be a regular digraph with radius s. Then D is a radially Moore digraph if it has the maximum possible number of nodes and the diameter of D does not exceed s+1. We show that for each s and t there exists a regular radially Moors digraph of degree t with radius s. Moreover, we give an upper bound for the number of central nodes in radially Moore digraphs with degree two.