A Balanced Signed Digraph
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We extend a balanced signed graph to a digraph, and present a necessary and sufficient condition for a signed digraph to be balanced. Moreover, we give another necessary and sufficient condition for a signed digraph \((D,w)\) to be balanced by using zeta functions of \(D\). As an application, we discuss the structure of balanced coverings of signed digraphs under consideration of coverings of strongly connected digraphs.
KeywordsBalanced signed digraph Strongly connectivity Covering Zeta function
We would like to thank the referee for many valuable comments and many helpful suggestions.
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