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So far, many problems of the primitive exponent of traditional single nonnegative matrix have been resolved. Currently, pushing traditional single nonnegative matrix to matrix pairs which have relatively application in many areas such as information science, communication networks, computer science, is a new trend. According to correspondence relation, two-colored digraphs can be used to solve matrix problems. We consider the uncolored digraph of two-colored digraph has vertices and none non-common arc. The range of exponents and extremal two-colored digraphs are given.

The Range of Exponents of Special Two-Colored Digraph with One Non-Common Arc