The Primitive Exponent Set of a Class of Representative Twocolored Digraph in Graph Theory

Abstract

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