Upper Bound of Primitive Exponent of a Class of Nonnegative Matrix Pairs

Abstract

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 n vertices and consists of one n − cycle and one m − cycle are considered. The upper bound of exponent and characteristic of extreme two-colored digraphs are given.