Coloring of a Digraph
Sampathkumar, E.
Original · EN
A coloring of a digraph D=(V,E) is a coloring of its vertices following the rule: Let uv be an arc in D. If the tail u is colored first, then the head v should receive a color different from that of u. The dichromatic number χd(D) of D is the minimum number of colors needed in a coloring of D. Besides obtaining many results and bounds for χd(D) analogous to that of chromatic number of a graph, we prove χd(D)=1 if D is acyclic. New notions of sequential colorings of graphs/digraphs are introduced. A characterization of acyclic digraph is obtained interms of L-matrix of a vertex labeled digraph.
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