含三个圈的本原不可幂定号有向图的基  

Bases of Primitive Non-powerful Signed Digraphs with Three Loops

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：《河北北方学院学报（自然科学版）》2011年第4期6-10,共5页Journal of Hebei North University:Natural Science Edition

基　　金：山西省自然科学基金资助项目(2008011009)

摘　　要：为了深入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.通过运用对图的特点和规律进行分析的方法,即有两个圈长度相同,且都与第三个圈长度不同.首先通过利用有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集、本原指数、"异圈对"、途径、歧义指数、图的直径等相关理论知识,讨论了在这两类图中是否存在所需的途径对,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.The bases of a clas to comprehensively understand its graph, the first and second loops Firstly, the upper bounds of the s of primitive non-powerful signed digraphs with three loops are studied relevant properties. By analyzing the characteristics and rules of this diof three loops have the same length which is different with the third. bases are obtained with some lemmas and definition of non-powerful signed digraphs. Then by using the related knowledge of Frobenius set, primitive exponent, distinguished cycle pair, SSSD walks, ambiguity index, the diameter of digraph and apagoge, the existence of SSSD walks needed in the two digraphs is discussed. Precise value of the bases of primitive non-powerful signed digraph which contains three loops is 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]