只含n-1圈和n-2圈的n阶本原有向图的m-competition指数  

The m-competition indices of all primitive digraphs of order n only with(n-1)-cycles and(n-2)-cycles

作　　者：刘彩锋 高玉斌[1] 

机构地区：[1]中北大学理学院,太原030051

出　　处：《黑龙江大学自然科学学报》2016年第1期41-49,共9页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11071227);山西省留学回国人员科研资助项目(2012-070)

摘　　要：设D是一个n阶本原有向图,对于正整数m和n(1≤m≤n),本原有向图D的m-competition指数(简记为km(D))定义为最小正整数k,满足:对于D中任意一对顶点x和y,存在m个不同的顶点,使得从顶点x和y到这m个不同的顶点都有k长的途径。研究只含n-1圈和n-2圈这两种圈长的所有n阶本原有向图,对每个本原有向图中,任一点经过k长途径所到达的顶点的集合,以及顶点的个数进行分析,根据m和n的关系,再结合m-competition指数的定义,得到所有这些本原有向图的m-competition指数。Let D be a primitive digraph of order n,for positive integers m and n with 1≤m≤n,the mcompetition index of the primitive digraph D,denoted by km（D）,is defined as the smallest positive integer k such that for every pair of vertexes x and y in D,there exist m distinct vertexes such that there exist walks of length k from x and y to the m distinct vertexes.All primitive digraphs of order n only with（n-1）-cycles and（n-2）-cycles are discussed.The sets and the numbers of vertexes which are formed by every vertex passing a walk of length k in every primitive digraph are researched.In addition,based on the relation m and n and the definition of m-competition index,the m-competition indices of all these primitive digraphs are obtained.

关 键 词：本原有向图 本原指数 m-competition指数 

分 类 号：O157.5[理学—数学]