2-Competition Index of Primitive Digraphs Using Graph Theory

Recently,scrambling index and competition index are widely applied to stochastic matrices and food webs. By analyzing the relationship of scrambling index and 2-competition index,n-「d/2」+ 1 was proved to be an upper bound of the 2-competition2 index of a primitive digraph with exact d loops in this article.Moreover,the maximum index problem and the index set problem for the 2-competition index of primitive digraphs with minimally strong digraphs were settled.

n阶本原极小强连通有向图k-指数的最小值

本文证明了:当1≤k≤︱n/4︱时,n阶本原极小强连通有向图k指数的最小值是4。

恰含两圈长的n阶本原极小强连通有向图的广义指数集

本文得到了恰含两个圈长的本原极小强连通有向图的1-顶点指数集

本原极小强连通有向图1-指数的下界

本文给出了n阶本原极小强连通有向图1-指数的下图:expD(1)4.且这个下界是可以达到的.

围长为2的奇数阶本原极小强连通有向图的1-指数集

研究了围长为2的n阶本原极小强连通有向图的1-指数集,证明了当n(≥5)为奇数时,En(1)={4,5,6,7,…,2n-5},无缺数段。