一类双色有向图的本原指数  

Exponents of a Class of Two-Colored Digraphs

作　　者：康育会[1,2] 王建中[1] 胡红萍[1] 

机构地区：[1]中北大学,山西太原030051 [2]长治医学院,山西长治046000

出　　处：《太原师范学院学报（自然科学版）》2010年第1期1-4,共4页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(60773131);山西省自然科学基金(2008011010)

摘　　要：一个双色有向图D是本原的,当且仅当存在非负整数h,k,且h+k>0,使得D的每一对顶点(i,j)都存在从i到j的(h,k)-途径,称h+k的最小值为D的本原指数.文章研究了一类特殊的双色有向图,其未着色图含有n个2-圈和2个m-圈,对其着色进行了分类,研究了所给类的本原性,并给出了本原指数的上界.A two-colored directed graph is primitive if and only if there exists 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 exponent of D,denoted exp（D） ,is the smallest value of h＋k over all such h and k. In this paper, we consider the special two-colored digraphs whose uncoloed digraph consists of n 2-cycles and two m-cycles, we class its colored digraphs and figure out wether it is primitive, studying the tight upper bound on the exponents.

关 键 词：本原指数 双色有向图 圈矩阵 

分 类 号：O157.5[理学—数学]