含有两个三圈的三色有向图的本原指数  

Exponents of a Class of Three-colored Digraphs

作　　者：林建青[1] 高玉斌[1] 

机构地区：[1]中北大学数学系,山西太原030051

出　　处：《太原师范学院学报（自然科学版）》2008年第4期12-14,共3页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：山西省自然科学基金(2007011017;2008011009)

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.文章研究一类其未着色图含一个3m+1-圈和两个3-圈的三色有向图,我们研究了该图的本原性,并给出了本原指数的一个可达的上界.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 primitive exponent of the three-colored digraph D is the minimum value of h ＋k＋l taken over all such h,k and l. We consider the special three-colored digraphs whose uncolored digraph consists of one 3m＋1-cycle and two 3-cycles. We study their primitive conditions ,and the tight upper bound on the exponents is given.

关 键 词：三色有向图 本原性 本原指数 

分 类 号：O157.5[理学—数学]