The Bases and Base Set of Primitive Symmetric Loop-Free Signed Digraphs |
Received:August 08, 2010 Revised:January 12, 2011 |
Key Words:
primitive signed digraph symmetric non-powerful base.
|
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.10901061; 11071088) and the Zhujiang Technology New Star Foundation of Guangzhou (Grant No.2011J2200090). |
|
Hits: 2764 |
Download times: 2218 |
Abstract: |
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. |
Citation: |
DOI:10.3770/j.issn:2095-2651.2012.03.006 |
View Full Text View/Add Comment |