一类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.定义h+k的最小值为双色有向图D的本原指数.研究了一类双圈双色有向图,给出了该双色有向图的本原条件和本原指数的上界,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 a （h,k）-path from i toj in D and the minimum value of （h＋ k） is defined as the exponent of the primitive two-colored digraph. In this paper, a class of two-colored digraphs with two cycles is studied, some primitive conditions of a two-colored digraph D and the upper bound of the exponents are given, and the extremal two-colored digraphs are characterized.