A Balanced Signed Digraph

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 $$(D,w)$$(D,w) to be balanced by using zeta functions of $$D$$D. As an application, we discuss the structure of balanced coverings of signed digraphs under consideration of coverings of strongly connected digraphs.

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