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).
Author NameAffiliation
Shuyong YI School of Mathematical Science, South China Normal University, Guangdong 510631, P. R. China 
Lihua YOU School of Mathematical Science, South China Normal University, Guangdong 510631, P. R. China 
Yuhan WU School of Mathematical Science, South China Normal University, Guangdong 510631, P. R. China 
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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
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