A balanced signed digraph
\textit{F. Harary} [Mich. Math. J. 2, 143--146 (1954; Zbl 0056.42103)] defined a balanced signed graph and presented a necessary and sufficient condition for a signed graph to be balanced. \textit{I. Sato} [Electron. J. Comb. 13, No. 1, Research paper R91, 12 p. (2006; Zbl 1114.05084)] studied a factorization of the weighted zeta function of an (irregular or regular) covering of a graph by equivalence classes of prime, reduced cycles of the base graph, and discussed the structure of balanced covering of signed graphs. Motivated by these results, they extended a balanced signed graph to a digraph, and presented a necessary and sufficient condition for a signed digraph to be balanced. Furthermore, they given another characterization for a signed digraph \((D, w)\) to be balanced by using the weighted Ihrar zeta function and the Ihara zeta function of \(D\). At the end, authors studied the structure of balanced covering of a digraph. This paper is worth reading. It will useful to researcher on signed graph .
scientific article; zbMATH DE number 6521736
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