具有三个圈的本原不可幂定号有向图的基指数

Bases of primitive non-powerful signed digraphs with three laps

通过研究本原不可幂定号有向图基的相关性质,对具有三个圈的本原不可幂定号有向图的基指数进行了研究.通过对于图的特点及规律进行分析的方法,即有两个圈长度相同,并且其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的值,再运用反证法并综合运用集、本原指数、"异圈对"、途径、歧义指数以及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要的SSSD途径对,从而得出了具有三个圈的本原不可幂定号有向图的基指数的确切值.

In this paper,the bases of a class of primitive non-powerful signed digraphs with three laps are studied.Byanalyzing 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 non-powerful signed digraphs.Then it uses the related knowledge of Frobenius set,primitive exponent,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 with three laps are obtained.