一类n阶本原图的广义Competition指数

Generalized competition indexes of a class of primitive digraphs of order n

根据图论、数论的相关知识,对本原图中每一点经过k长途径所到达点的集合进行分析,再结合广义Competition指数的定义,确定了一类n阶本原图的广义Competition指数.当m≤s+1且s+m为奇数时,km(D)=1+((s+m-1)/2)s,当m≤s且s+m为偶数时,km(D)=1+((s+m-1)/2)(s+1);当m≥s+2时,km(D)=1+s2.

Based on the related knowledge of graph theory and number theory, the set formed by the vertexes was analyzed, which arrived by every vertex passing a walk of length k in a primitive digraph. Then combined with the definition of generalized competition index, the generalized competition indexes of a class of primitive digraphs of ordern was determined.If m≤s＋1 and s＋m is odd,km（D）=1＋〔s＋m-1/2〕s;if m≤s and s＋m in even,km（D）=1＋〔s＋m-2/2〕（s＋1）;if m≥s＋2时,km（D）=1＋s2.