两类本原不可幂定号有向图基的界

Bounds of the Bases on Two Classes of Primitive Non-Powerful Signed Digraphs

利用图论和矩阵理论的方法,讨论了两类本原不可幂定号有向图,研究了仅有两个圈的本原不可幂定号有向图Ds,t和其中有两个圈长相同但仅有三个圈的不可幂定号有向图Ds,t,q的基的界,利用定号有向图基的定义和Frobenius数得到了仅有两个圈的本原不可幂定号有向图Ds,j的基,刻划了定号有向图Ds,t,q基的界.

By using graph theory and matrix theory,two classes of primitive non-powerful signed digraphs were discussed.The bounds of the bases of the primitive non-powerful signed digraphs Ds,t with two cycles and those with three cycles in which two cycles have the same length were researched.By using the definition of the base of signed digraphs and the Frobenius number,the bases on the signed digraphs Ds,t were obtained and the bounds of the bases on the signed digraphs Ds,t,q were characterized.