  We extend the Grundy number and the ochromatic number, parameters on graph
colorings, to digraph colorings, we call them {\emph{digrundy number}} and
{\emph{diochromatic number}}, respectively. First, we prove that for every
digraph the diochromatic number equals the digrundy number (as it happen for
graphs). Then, we prove the interpolation property and the Nordhaus-Gaddum
relations for the digrundy number, and improve the Nordhaus-Gaddum relations
for the dichromatic and diachromatic numbers bounded previously by the authors
in [Electron. J. Combin. 25 (2018) no. 3, Paper {\#} 3.51, 17 pp.]
