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

作　　者：张洁敏[1] 高玉斌[1] 

机构地区：[1]中北大学数学系,山西太原030051

出　　处：《湖南文理学院学报（自然科学版）》2014年第1期4-6,15,共4页Journal of Hunan University of Arts and Science(Science and Technology)

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

摘　　要：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.

关 键 词：本原图 途径 广义competition指数 

分 类 号：O157.5[理学—数学]