Abstract
Graph is simple and intuitive. It can be used to solve many problems in computer science. For a kind of representativedigraph, the edges (arcs) of the digraph are colored with red and blue colors. The range of the primitive exponent are discussed indifferent cases, and the extremal two-colored digraphs are found by coloring all arcs with two colors. Finally, the primitive exponentset is given. The results can provide a reference for the study of primitive exponent of three-colored digraph and the application ofgraph coloring in computer science, such as communication network and coding cache.
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