含有两个三圈的三色有向图的本原指数

一个三色有向图D是本原的，当且仅当存在非负整数h，k和l，且h＋k＋l〉0，使得D中的每一对顶点（i，j）都存在从i到j的（h，k，l）-途径，并称h＋k＋l的最小值为D的本原指数．文章研究一类其未着色图含一个3m＋1-圈和两个3-圈的三色有向图，我们研究了该图的本原性，并给出了本原指数的一个可达的上界．

Exponents of a Class of Three-colored Digraphs

A three-colored digraph D is primitive if and only if there exist nonnegative integers h,k and l with h k l>0 such that for each pair(i,j) of vertices there exists an(h,k,l)-walk in D from i to j.The primitive exponent of the three-colored digraph D is the minimum value of h k l taken over all such h,k and l.We consider the special three-colored digraphs whose uncolored digraph consists of one 3m 1-cycle and two 3-cycles.We study their primitive conditions,and the tight upper bound on the exponents is given.