无环的本原反对称带号有向图的基指数集  

The Base Set of Primitive Anti-Symmetric Signed Digraph with No Loops

作　　者：程峰[1] 尤利华[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）》2012年第4期13-19,共7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项目(2011J2200090)

摘　　要：研究了图类n阶无环的本原反对称带号有向图的基指数,证明了其最大基指数为2n-1,刻画了达到上界的极图.设C是带号有向图S中长为l的圈,引入记号dl,以dl和l为参数,得到了带号有向图S的基指数的一个上界.按dl的取值分类讨论,应用图论方法和已得的上界,完全确定了n阶无环的本原反对称带号有向图的基指数集.The basis of primitive anti - symmetric signed digraphs with no loops on n vertices is studied, the maxi- mum base is obtained and the extreme signed digraphs with the maximum base is characterized. Let S be a signed digraph, and C be a cycle of S with length l, notation d1 be defined, then an upper bound for the base of S is ob- tained by two parameters d2 and l. According to the value of d1, the base set of primitive anti - symmetric signed di- graphs with no loops on n vertices is completely determined by the method of graph theory and known upper bound.

关 键 词：本原 反对称 带号有向图 不可幂 基指数 

分 类 号：O151.21[理学—数学]