一类含奇数个顶点的三色有向图的本原指数  

Exponents of a Class of Three-Colored Digraphs with Odd Vertices

作　　者：王玉香[1] 雷英杰[1] 王建中[1] 

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2008年第3期201-205,共5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(2007011017)

摘　　要：一个三色有向图D是本原的,当且仅当存在非负整数h,k和l,且h+k+l>0,使得D中的每一对顶点(i,j)都存在从i到j的(h,k,l)-途径,并称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,其含有奇数个顶点,其未着色图恰含一个n-圈、一个(n-2)-圈和一个2-圈,给出了在一种本原条件下的三色有向图本原指数紧的上界.A three-colored digraph D is primitive if and only if there exist nonnegative integers h,k and l with h＋k＋l〉0 such that for each pair （i,j） of vertices there exists an （h ,k ,l）-walk in D from i to j. The exponent of the primitive three-colored digraph D is the minimum value of h＋k＋l taken over all such h,k and 1. The special three-colored digraphs with odd vertices whose uncolored digraph consists of one n-cycle, one （n-2）-cycle and one 2-cycle. The exponent of compact supper bound for one three-colored primitive digraph is given.

关 键 词：三色有向图 本原指数 弧 圈矩阵 

分 类 号：O157[理学—数学]