尤利华,易叔勇.具有第二大基指数的本原对称带号有向图的刻画[J].数学研究及应用,2013,33(4):379~391
具有第二大基指数的本原对称带号有向图的刻画
The Characterization of Primitive Symmetric Signed Digraphs with the Second Maximum Base
投稿时间:2012-02-09  最后修改时间:2012-10-09
DOI:10.3770/j.issn:2095-2651.2013.04.001
中文关键词:  矩阵  对称  本原  不可幂  基指数  带号有向图.
英文关键词:matrix  symmetric  primitive  non-powerful  base  signed digraph.
基金项目:国家自然科学基金(Grant Nos.10901061; 11071088), 广州市珠江科技新星项目(Grant No.2011J2200090), 广东省国际科技合作创新平台项目(Grant No.2012gjhz0007).
作者单位
尤利华 华南师范大学数学科学学院广东 广州 510631 
易叔勇 华南师范大学数学科学学院广东 广州 510631 
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中文摘要:
      最近,具有第一大基指数$2n$的$n$阶本原对称带号有向图和具有第一大基指数$2n-1$的$n$阶本原对称无环的带号有向图分别得到了刻画.本文首先刻画了具有基指数$2n-1$的$n$阶本原对称带环的带号有向图,进而给出了具有第二大基指数$2n-1$的$n$阶本原对称带号有向图的刻画.
英文摘要:
      Recently, the primitive symmetric signed digraphs on $n$ vertices with the maximum base $2n$ and the primitive symmetric loop-free signed digraphs on $n$ vertices with the maximum base $2n-1$ are characterized, respectively. In this paper, the primitive symmetric signed digraphs with loops on $n$ vertices with the base $2n-1$ are characterized, and then the primitive symmetric signed digraphs on $n$ vertices with the second maximum base $2n-1$ are characterized.
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