一类本原不可幂定号有向图的基

The Bases of a Class of Primitive Non-powerful Signed Digraphs

本原不可幂定号有向图S的基指数l(S)是指最小的正整数l,使得在S中,从任意一点u到任意一点v都存在一对长为l的SSSD途径。本文对一类包含3个圈的本原不可幂定号有向图进行研究。通过讨论图中从任意一点u到任意一点v是否存在SSSD途径,从而得到了此类图的基的上界,再运用反证法求得了这类图的基。进一步讨论得到了另一类包含3个圈的本原不可幂定号有向图的基。

The base of a primitive non-powerful signed digraphS, denoted by X, is a least integer Xλ such that there is a pair of SSSD walks of length {Aλ} from each vertex Aλ to each vertex v in S. In this work, the bases of a class of primitive non-powerful signed digraphs that contain three circles are studied. First through the discussion of whether there is a pair of SSSD walks from each vertex Aλ to each vertex v in the digraph, we get the upper bound of the bases. Then by using the proof by contradiction, we get the value of the bases. We also obtain the bases of another class of primitive non-powerful signed digraphs that contain three circles.