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Graphs and Combinatorics

, Volume 31, Issue 6, pp 2215–2230 | Cite as

A Balanced Signed Digraph

  • Yusuke Higuchi
  • Iwao Sato
Original Paper

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.

Keywords

Balanced signed digraph Strongly connectivity Covering  Zeta function 

Notes

Acknowledgments

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

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Mathematics Laboratories, College of Arts and SciencesShowa UniversityFujiyoshidaJapan
  2. 2.Oyama National College of TechnologyOyamaJapan

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