含三个圈的本原不可幂定号有向图的基  

Bases of Primitive Non-powerful Signed Digraphs

作　　者：王宁[1] 邵燕灵[1] 

机构地区：[1]中北大学数学系,山西太原030051

出　　处：《西安文理学院学报（自然科学版）》2011年第3期6-9,共4页Journal of Xi’an University(Natural Science Edition)

基　　金：山西省自然科学基金资助项目(2008011009)

摘　　要：为了进一步了解本原不可幂定号有向图基的相关性质,对含有三个圈的本原不可幂定号有向图的基进行了研究,通过对图的特点和规律进行分析,即有两个圈长度相同,且都与第三个圈长度不同,首先通过利用用关本原不可幂定号有向图的引理及定义得到基的上界,再运用反证法并综合运用Frobenius集、本原指数、"异圈对"、SSSD途径、岐义指数、图的直径等相关理论和知识,讨论了在这两类图中是否存在所需的SSSD途径对,从而得出了含有三个圈的本原不可幂定号有向图的基的精确值.In this paper, we study the bases of a class of primitive non - powerful signed di- graphs with three laps. By analyzing this digraph, two laps of three circle have the same length. Firstly, the upper bounds of the bases are obtained with some lemmas and definition of nonpowefful signed digraphs. Then we use the related knowlege of Frobenius set, primitive exponet,distinguished cycle pair. SSSD walks. Ambiguity index, the diameter of digraph and apagoge, etc. Precise value of the bases of primitive non - powerful signed digraph which contains three laps are obtained.

关 键 词：本原指数 SSSD途径对 基 定号有向图 

分 类 号：O157.5[理学—数学]