围长为r的n阶本原有向图的点指数  

The vertex exponent of primitive diagraph of order n with girth r

作　　者：王龙芹[1] 檀江华[1] 秦峰[1] 孙苗苗[1] 

机构地区：[1]滁州学院数学系,安徽滁州239012

出　　处：《纯粹数学与应用数学》2010年第4期626-629,共4页Pure and Applied Mathematics

基　　金：国家自然科学基金(10871166);安徽省高校优秀青年人才基金(2009SQRZ144);滁州学院大学生科研项目(2009xs019)

摘　　要：研究本原有向图的顶点指数,运用图论与数论方法,得到了n阶围长为r的本原有向图的点指数expD(k)的上界:若rn,且r为素数,D∈Dn,r={D|D为n阶本原有向图且围长为r},则expD(n,k)=rn-2r+k(1≤k≤n);若r|n,且r为素数或素数的幂,D∈Dn,r,则expD(n,1)=rn-3r+2.This paper discusses the vertex exponent for the class of primitive diagraph.By using graph theoretical methods and combinatorial method,it proves that the maximum value of vertex exponent of primitive diagraph of order n with girth r is as follows：if r n,r is a prime number,and D is a primitive diagraph of order n with girth r,then expD（n,k） = rn-2r ＋ k（1 ≤ k ≤ n）;if r ｜ n,r is a prime number or its positive power,and D is a primitive diagraph of order n with girth r,then expD（n,1） = rn-3r ＋ 2.

关 键 词：本原有向图 Frobenius数 点指数 

分 类 号：O157.5[理学—数学]