一类特殊双色有向图的本原指数

Primitive exponents of a class of special 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,且h+k>0,使得D中的每对顶点(i,j),都存在从i到j的(h,k)途径.将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条件和指数上界,并对极图进行了刻画.

A two-colored digraph D is primitive if there exist nonnegative integers h and k with h＋k〉0 such that for each pair （i,j） of vertices there exists an （h,k）-path in D from i to j. The exponent of the primitive two colored di graph D is the minimum value of h＋k taken over all such h and k. In this paper, some primitive conditions and an upper bound on the exponents are given, and the extremal of two-colored digraphs is characterised.