一类特殊的三色有向图的本原指数  

Exponents of Class of Special Three-Colored Digraphs

作　　者：李娟[1] 邵燕灵[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2期1-5,共5页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：国家自然科学基金(10571163);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,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.文章研究一类特殊的三色有向图,其未着色图恰含一个n-圈、一个3-圈和一个4-圈,我们研究了该图的本原性并给出了在一种本原条件下的三色有向图的本原指数.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 l. We consider the special three-colored digraphs whose uncolored digraph consists of one n-cycle,one （n-1）-cycle and one 3-cycle. We study the primitive conditions and give the exponent for the three-colored primitive digraph.

关 键 词：三色有向图 本原条件 本原指数 

分 类 号：O157[理学—数学]