Abstract
Sampathkumar [F. Harary, Graph Theory (Addison-Wesley, Reading, MA, 1969)] defined the coloring of a digraph [Formula: see text] as a coloring of its vertices by the following rule: Let [Formula: see text] be an arc in [Formula: see text]. If the tail [Formula: see text] is colored first, then the head [Formula: see text] should receive a color different from that of [Formula: see text]. But, if [Formula: see text] is colored first, then [Formula: see text] may or may not receive the color of [Formula: see text]. The dichromatic number [Formula: see text] of a digraph [Formula: see text] is the minimum number of colors needed for coloring of a digraph [Formula: see text]. In this paper, we obtain some results on uniquely colorable digraphs and Nordhaus–Gaddum type results for digraphs.
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