一类本原有向图的m-competition指数

设D是一个n阶本原有向图, 对于正整数m及n(1≤m≤n), 定义本原有向图D的m competition指数为最小正整数k, 满足对于任意一对顶点x和y, 在D中都存在m个不同的顶点v1,v2,…,vm,使得xkvi且ykvi(i=1,2,…,m).文中讨论了一个含有两个n-2圈和一个n-3圈的n阶本原有向图D。由D的结构得到本原有向图Dn-2和Dn-3, 再根据m-competition指数的定义, 得到这个本原有向图D的m-competition指数。

m-competition index of a kind of primitive digraph

Let D be a primitive digraph of order n.For positive integers m and n(1≤m≤n), we define its m competition index,km(D), as the smallest positive integer k that satisfies the condition that for every pair of vertices x and y, there are m different vertices v1,v2,…，vm in D that satisfy xkvi and ykvi(i=1,2,…，m). We address a primitive digraph D of order n with two (n-2) cycles and one (n-3) cycle. We derive primitive digraphs Dn-2 and Dn-3 based on the structure of D. We can further obtain m-competition index of the primitive digraph D based on the definition of m-competition index.