摘要
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中的每一对顶点(i,j)都存在从i到j的(h,k)-途径,则称h+k的最小值为D的本原指数.本文考虑了一类特殊的双色有向图,它的未着色图有(m+n)个顶点,包含一个m-圈和一个n-圈,给出了本原条件和指数上界,并对达到指数上界的极图进行了刻划.
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）-walk in D from i to j. The special two- colored digraphs whose uncolored digraph has m＋n vertices and consists of one m-cycle and one n-cycle are considered. Some primitive conditions and the upper bound of the exponents are given. The characterizations of extremal two-colored digraphs are also given.
出处
《中北大学学报（自然科学版）》
EI
CAS
2007年第5期377-382,共6页
Journal of North University of China(Natural Science Edition)
基金
国家自然科学基金资助项目(10571163)
山西省自然科学基金资助项目(20041010)
关键词
双色有向图
本原指数
极图
two-colored digraph
primitive exponent
extremal digraph
