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A Balanced Signed Digraph

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Abstract

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.

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Acknowledgments

We would like to thank the referee for many valuable comments and many helpful suggestions.

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Authors and Affiliations

  1. Mathematics Laboratories, College of Arts and Sciences, Showa University, 4562 Kamiyoshida, Fujiyoshida, Yamanashi, 403-0005, Japan

    Yusuke Higuchi

  2. Oyama National College of Technology, Oyama, Tochigi, 323-0806, Japan

    Iwao Sato

Authors
  1. Yusuke Higuchi
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  2. Iwao Sato
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Corresponding author

Correspondence to Iwao Sato.

Additional information

This research was partially supported by Grant-in-Aid for Science Research (C).

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Higuchi, Y., Sato, I. A Balanced Signed Digraph. Graphs and Combinatorics 31, 2215–2230 (2015). https://doi.org/10.1007/s00373-014-1496-z

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  • DOI: https://doi.org/10.1007/s00373-014-1496-z

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