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中文摘要：
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。
英文摘要：
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.
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