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中文摘要：
如果存在正整数k使得对于D中任意两点u和V（允许仳=u），在D中都有从仳到V的长为k的有向途径，则称有向图D是本原的．给有向图的每条弧赋以符号＋1或者-1得到的图S称为带号有向图．如果带号有向图S中包含SSSD途径对，即包含两条有相同的起点，相同的终点，相同的长度，并且有不同的符号的途径对，则称S是不可幂的．在本文中，我们将LewinM提出的lewin数的概念从本原有向图推广到本原不可幂带号有向图，给出了本原不可幂带号有向图S的lewin数2（S）的若干上界，并提出了一个公开问题．
英文摘要：
A digraph D is primitive if for some positive integer k there is a walk of length exactly k from each vertex u to each vertex v （possible u again）. A signed digraph S is a digraph where each arc of S is assigned a sign 1 or -1. A signed digraph S is non-powerful if S contains a pair of SSSD walks which they have the same initial vertex, same terminal vertex and same length, but different signs. In this paper, we study lewin number l（S） for a primitive non-powerful signed digraph S, which is a generalization of lewin number for a primitive digraph introduced by Lewin M, some upper bounds on l（S） are given, and an open problem is presented.
同期刊论文项目
同项目期刊论文
Primitive non-powerful symmetric loop-free signed digraphs with given base and minimum number of arc
On a conjecture about primitive non-powerful symmetric loop-free signed digraphs with base 3 and min
The Generalized (Terminal)Wiener Polarity Index of Generalized Bethe Trees and Coalescence of Rooted
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