The Characterization of Primitive Symmetric Signed Digraphs with the Second Maximum Base
Received:February 09, 2012  Revised:October 09, 2012
Key Word: matrix   symmetric   primitive   non-powerful   base   signed digraph.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.10901061; 11071088), the Zhujiang Technology New Star Foundation of Guangzhou (Grant No.2011J2200090) and Program on International Cooperation and Innovation of Guangdong Province Education Department (Grant No.2012gjhz0007).
Author NameAffiliation
Lihua YOU School of Mathematical Sciences, South China Normal University, Guangdong 510631, P. R. China 
Shuyong YI School of Mathematical Sciences, South China Normal University, Guangdong 510631, P. R. China 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:2095-2651.2013.04.001
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