一类恰含一个3-圈的三色本原有向图指数上界

Upper Bound of Exponent of a Class of Primitive Three Colored Digraphs with One 3-cycle

在传统(单个)非负本原矩阵的基础上,将非负本原矩阵对的研究推广到非负本原矩阵簇,是组合矩阵论中一个崭新的研究内容.事实上,非负矩阵簇可以与多色有向图建立一一对应关系,从而把矩阵的问题转化为图的问题进行研究.该文研究了一类三色本原有向图,它的未着色图中包含n个顶点,一个n-圈、一个(n-1)-圈和一个3-圈,给出本原条件和指数上界.

On the basis of research of traditional primitive （single） nonnegative matrix, the nonnegative primitive matrix pairs, extended to the nonnegative primitive matrix cluster, is a brand-new research in combinatorial matrix theory. In fact, there is a one-to-one relationship between nonnegative primitive matrix cluster and multi-colored digraph, so the problem of matrices can be changed into that of graphics to be solved. In this paper, a class of primitive three-colored digraphs is analyzed, and its uncolored digraph has n vertices, consisting of one n-cycle, one （n - 1） -cycle and one 3-cycle. Some primitive conditions and the tight upper bound of primitive exponents are given.