一类三色有向图的本原指数

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.研究了一类特殊的三色有向图,其未着色图恰含一个n-圈、一个(n-1)-圈和一个2-圈,研究了该图的本原性,并给出了在一种本原条件下的三色有向图的本原指数.

A three-colored digraph D is primitive if and only if there exist nonnegative integers h,k and l with h＋k＋l0 such that for each pair（i,j） of vertices there exists an（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.It is considered the special three-colored digraph whose uncolored digraph consists of one n-cycle,one n-1-cycle and one 2-cycle.The primitive conditions are studied,and the exponent for one three-colored primitive digraph is given.