某类本原不可幂定号有向图基的界

Bounds on the bases of the Class Primitive Non-Powerful Signed Digraphs

对于某类含有三个圈和四个圈的本原不可幂定号有向图的基进行了研究。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类图中是否存在所需的SSSD途径对,从而可得其下界。若上界与下界相等,则可得到其基的具体值。

In this work, we study the bases of a kind of primitive non-powerful signed digraphs with three and four simpe cycles. The upper bounds of the bases are obtained with some lemmas and definition of the primitive non-powerfal signed digraphs. Then the lower bounds of the bases are obtained through discussing whether there is a pair of SSSD walks in digraphs by using knowledge about ＂distinguished cycle pair＂, Frobenius set, primitive exponent. If the upper bounds are equal with the lower bounds, the specific value of the bases are obtained.