一类有环的双色有向图的本原指数

摘要

A two - colored digraph D is primitive if, and only if there exist nonnegative integers h and k with h ＋ k 〉 0 such that for each pair （ i ; j） of vertices, there exists an （ h ; k） - walk in D from i to j. The expo- nent of the primitive two - colored digraph D is the minimum value of h ＋ k taken over all such h and k. In this paper,the exponents of a class of two - colored digraphs with loops is taken into consideration, and hence, the primitive conditions and the upper bounds on the exponents are obtained.%一个双色有向图的D是本原的,当且仅当存在非负整数h和k,且h＋k〉0,使得D中的每一对顶点（i,j）都存在从i到j的（h,k）途径,此时称h＋k的最小值为D的本原指数.利用代数与图论的方法,研究一类带有环的双色有向圈的本原指数,给出了本原指数和本原指数上界。