Abstract
There is a one-to-one relationship between nonnegative matrix pairs and two-colored digraph. With the knowledge of graph theory, by studying the associated directed digraph of a class of special nonnegative matrix pairs, that is a class of two-colored digraphs whose uncolored digraph have 3n-1 vertices and consists of one (3n-1)-cycle and one n-cycle are considered. The exponent and characteristic of extreme two-colored digraphs are given.
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