某类本原不可幂定号有向图的基指数

Base Exponents of Primitive Non-powerful Signed Digraph

为了进一步了解本原不可幂定号有向图的基的特点及有关性质,对一个特殊的本原不可幂定号有向图的基进行了研究.通过分析这个图的特点,此图含有三个圈,其中两个圈长相等.运用反证法并结合图中的本原指数、点指数、基指数、Frobenius集、可幂与不可幂及"异圈对"等相关定义及性质加以证明.假定圈长相等的两个圈的符号相同或不同,讨论在这两种情况下所需的SSSD途径对,证得基的上界与下界,并且二者相等,由此得出这类图的基指数的具体值.

To further understand characteristics and properties of the bases of primitive non-powerful signed digraph,a primitive non-powerful signed digraph with three loops are studied.By analyzing the features of the digraph in which there are two loops that have equal lengths,using apagoge and knowledge about primitive exponents,point exponents,bases exponents,Frobenius set,powerful,non-powerful and ＂distinguished loops pair＂,assuming that the two loops with equal lengths have the same or different signs and discussing SSSD walks,the equal upper and lower bounds of bases are obtained,and then the true values of base exponents are got.