期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
The Local Bases of a Class of Primitive Nonpowerful Signed Digraphs
摘要/Abstract
为了更进一步了解本原不可幂定号有向图的local基的相关性质,对一类含有3个圈的特殊的本原不可幂定号有向图的第k个local基进行了研究.首先利用相关文献所提及的关于本原不可幂定号有向图的重要定义及其引理,确定出了此类本原不可幂定号有向图的本原指数.由于本图的特殊性,又对其各个圈的圈长及符号分情况进行了讨论,最后得到了这类本原不可幂定号有向图的第k个local基.主要运用"异圈对"、Frobenius集和本原指数等相关知识,以及反证法,详细地分析了这类图的第k个local基.
The kth local bases of a sepcial class of primitive nonpowerful signed digraphs with three cycles is studied to understand the character of primitive nonpowerful signed digraphs further.Firstly,the exponent of this class of digraphs with the important definition and lemmas about the primitive nonpowerful signed digraphs in some related articles is obtained.Then,according to this special digraph,the situation to discuss the length and sign of the cycles in the digraph is divided.Finally,the kth local bases of this class of primitive nonpowerful signed digraphs is obtained.By using knowledges about"distinguished cycle pair",Frobenius set,exponent,and also reduction to absurdity,the kth local bases of this class of digraph is analyzed.