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无环的本原反对称带号有向图的基指数集
  • 期刊名称：华南师范大学学报
  • 时间：0
  • 页码：13-19
  • 分类：O151.21[理学—数学;理学—基础数学]
  • 作者机构：[1]华南师范大学数学科学学院,广东广州510631
  • 相关基金：国家自然科学基金项目（10901061,11071088）; 广州市珠江科技新星项目（2011J2200090）
  • 相关项目：组合矩阵论中若干问题的研究
作者： 程峰|尤利华|
关键词： 本原, 反对称, 带号有向图, 不可幂, 基指数, primitive , anti - symmetric , signed digraph , non - powerful , base
中文摘要：

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.

英文摘要：

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.

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组合矩阵论中若干问题的研究
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