一个特殊本原不可幂定号有向图的基

Discussion on the Bases of a Special Primitive Non-powerful Signed Digraph

为了进一步了解本原不可幂定号有向图基的相关性质,对一个含有3个圈的特殊的本原不可幂定号有向图的基进行了研究。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,再运用反证法并结合图中的"异圈对"、Frobenius集及本原指数等相关知识,讨论了在这个图中是否存在所需的SSSD途径对,从而得到了这个图的基。

In order to know more about relative properties of the bases of the primitive non-powerful signed digraph,this paper makes the research on the bases of a special primitive non-powerful signed digraph with three cycles,obtains the upper bounds of the bases with some lemmas and definitions of the primitive non-powerful signed digraph,and by busing the proof by contradiction and connecting with ＂distinguished cycle pair＂,Frobenius set and other relative knowledge,discusses whether or not there is a pair of SSSD walks in digraph,and gets the bases of the digraph.