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The dichromatic number and the diachromatic number are generalizations of thechromatic number and the achromatic number for digraphs considering acycliccolorings. In this paper, we determine the diachromatic number of digraphsarising from the Zykov sum of digraphs that admit a complete $k$-coloring with$k=\tfrac{1+\sqrt{1+4m}}{2}$ for a suitable $m$. Consequently, the diachromaticnumber equals the harmonious number for every digraph in this family. Inparticular, we study the chromatic number, the diachromatic number, and theharmonious chromatic number of the Zykov sum of cycles.

Zykov sums of digraphs with diachromatic number equal to their harmonious number