一类含有两个m-圈的三色有向图的本原指数

对于一个三色有向图D,其本原的定义是指当且仅当存在非负整数h,k,l,并且有h+k+l0,使得对于D中的每一对顶点(i,j)都存在从i到j的(h,k,l)-途径,定义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bm-1-圈、二个m-圈,并且研究了该图在一种本原条件下的三色有向图的本原指数。

Primitive Exponents of a Class of Three-colored Digraphs with Two m -cycles

For a three-colored digraph D,it is primitive if and only if there exists nonnegative integers h,k,l with h+k+l>0 such that for each pair(i,j) of vertices there exists a(h,k,l) walk in D from i to j.We define the minimum value of h+k+l as the exponent of the primitive three-colored digraph D.Special three-colored digraphs were studied,whose uncolored digraph consists of one bm-1-cycle,two m-cycle,and the paper gave the exponents for one kind of three-colored primitive digraph.