一类双色有向图的本原指数

Primitive Exponents of a Class of Two-Colored Digraphs

一个双色有向图D是本原的,如果存在非负整数h和k,h+k>0,使得D的每对顶点(i,j),都存在从i到j的(h,k)-途径.对所有的h和k,h+k的最小值定义为双色有向图D的本原指数.给出了一类双色有向图的本原指数集,并对极图进行了刻化.

A two colored digraph D is primitive if there exist nonnegative integers h and k with h＋k 〉 0 such that for eaeh pair （i,j） of vertices there exists an （h,k） -walk in D from i to j . The exponent of the primitive two-colored digraph D is the minimumvalue of h ＋k taken over all such h and k. In this paper, we give the exponent set of a class of primitive two-colored digraphs,and the characterizations of the extremal two-colored digraphs.