一类含有奇数个顶点的三色有向图本原指数上界  

Upper Bound of Primitive Exponent of a Class of ThreeColored Digraphs with Odd Vertices

作　　者：罗美金[1] 侯宗毅[1] 李茜 

机构地区：[1]河池学院数学与统计学院,广西宜州546300 [2]山西运城农业职业技术学院基础部,山西运城044000

出　　处：《数学的实践与认识》2017年第4期209-216,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11161018);广西自然科学基金(2013GXNSFBA019022);广西高校科研项目(YB2014335;KY2015ZD103);山西省高等学校科技创新项目(2015113)

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v,且h+k+v>0,使得D中的每一对顶点(i,j)都存在从i到j的(h,k,v)-途径,h+k+v的最小值定义为三色有向图D的本原指数.研究了一类三色有向图,它的未着色图中包含2佗-4个顶点,一个n-圈、一个(n-2)-圈和一个2-圈,给出了本原指数上界.A three-colored digraph D is primitive if and only if three exists nonnegative integers h, k and v with h ＋ k ＋ v 〉 0 such that for each pair （i, j） of vertices there exists a （h, k, v）-walk in D from i to j. The exponent of the primitive three-colored digraph D is the minimum value of h ＋ k ＋ v taken over all such h, k and v. A class of three-colored digraphs were studied whose uncolored digraph has 2n - 4 vertices, consists of one n-cycle, one （n - 2） -cycle and one 2-cycle. The tight upper bound on the primitive exponent were given.

关 键 词：三色 有向图 本原 指数 上界 

分 类 号：O157.5[理学—数学]