本原有向图D_(n,q,s)的scrambling指数  

The Scrambling Index of Primitive Digraphs D_(n,q,s)

作　　者：尤利华[1] 陈芳[1] 

机构地区：[1]华南师范大学数学科学学院,广东广州510631

出　　处：《华南师范大学学报（自然科学版）》2013年第5期7-12,共6页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(10901061;11071088);广州市珠江科技新星专项资助项目(2011J2200090)

摘　　要：设n,q,s是正整数,满足1≤s<q≤n,g.c.d.(q,s)=1,且q+s≥n+1.定义有向图D n,q,s=(V,E),其中V={1,2,…,n},E={(i,i+1)1≤i≤n-1}∪{(s,1),(n,n-q+1)}.显然,D n,q,s是本原有向图,且是一类重要的极图.运用了数论和图论的方法得到了Dn,q,s的scrambling指数,根据本原有向图D的本原指数exp(D)与scrambling指数k(D)的已知结论,猜想lim n→∞k(D)exp(D)=1/2.Let n,q,s be integers,1 ≤s 〈q≤n,g. c. d. （q,s） = 1 ,and q ＋s≥n ＋ 1. Define the digraph Dn,q,s = （ V, E）, where V= {1,2,…,n} ,E= {（i,i＋1）｜1≤i≤n-1} ∪{（s,1）,（n,n-q＋1）}. Obviously, On,q,s a primitive digraph. In fact, Dn,q, s is an important extremal digraph. Scrambling index of On,q,s is studied by the method of Number theory and Graph theory. Moreover, based on the results of exponent exp（D） and scrambling index k（D） of the important primitive digraph D, conjecture lim n→∞k（D/exp（D）=1/2 ）is proposed.

关 键 词：本原有向图 SCRAMBLING指数 缺数段 指数集 

分 类 号：O151.21[理学—数学]