本原对称无环带号有向图的基指数与基指数集

The Bases and Base Set of Primitive Symmetric Loop-Free Signed Digraphs

中文关键词:  本原  带号有向图  对称  不可幂  基指数.

英文关键词:primitive  signed digraph  symmetric  non-powerful  base.

中文摘要:

      本文研究了$n$阶本原对称无环带号有向图的基指数和基指数集.我们得到了$n$阶本原对称无环带号有向图的基指数的上确界, 证明了其基指数集为$\{2, 3, \ldots, 2n-1\}$,并且给出了程、柳文中的一个重要结论的新证明.

英文摘要:

      In this paper, we study the bases and base sets of primitive symmetric loop-free (generalized) signed digraphs on $n$ vertices. We obtain sharp upper bounds of the bases, and show that the base sets of the classes of such digraphs are $\{2,3,\ldots , 2n-1\}$. We also give a new proof of an important result obtained by Cheng and Liu.