含有环的单双向间隔的双色有向圈的本原指数  

Exponents of Two-colored Single Double Interval Directed Cycles with Loops

作　　者：李雪香[1] 刘卫华[1] 高玉斌[1] 

机构地区：[1]中北大学理学院,太原030051

出　　处：《河南师范大学学报（自然科学版）》2011年第6期14-18,共5页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11071227);山西省自然科学基金(2008011009)

摘　　要：一个双色有向图D(A,B)是本原的,如果存在非负整数h和k,且h+k>0,使得D(A,B)中的每一对顶点(i,j)都存在从i到j的(h,k)途径,且称h+k的最小值为D(A,B)的本原指数.考虑一类特殊的双色有向图,它的未着色图有n个顶点,包含有一个n-圈,n-1/2个2-圈和n个环,给出了本原条件和指数上界.A two-colored digraph D（A,B） is primitive if there exist 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（A,B） from i to j. The exponent of the primitive two-colored digraph D（A,B） is the minimum value of h＋k taken over all such h and k. This article considers the special two-colored digraph whose uncolored digraph has n vertices and consist of one n-cycle , 2-cycles and n loops. The research gives some primitive conditions and the upper bounds on the exponents.

关 键 词：本原指数 本原有向图 双色有向图 

分 类 号：O157.5[理学—数学]