一类三角有向图的本原指数

Exponents of A Class of Three-colored Digraphs

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.对一类特殊的三色有向图进行了研究,其未着色图恰含一个n-圈、一个(n-2)-圆和一个3-圈,给出了一种本原条件下的本原指数,并对其所表达的本析指数进行了极图刻划.

A three-colored digraph D is primitive if and only if there exist nonnegative integers h,k and l with h＋k＋10 such that for each pair（i,j） of vertices there exists and（h,k,l）-walk in D from i to j.The exponent of the primitive three-colored digraph D is the minimum value of h＋k＋l taken over all such h,k and l.In this paper,we consider the special three-colored digraphs whose uncolored digraph consists of ne n-cycle,one n-2-cycle and one 3-cycle.We give some primitive conditions and a upper bound on the exponent.Further,we give the characterizations of extremal three-colored digraphs.