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Counting balanced signed graphs using marked graphs

Published online by Cambridge University Press:  20 January 2009

Frank Harary  and
Jerald A. Kabell
Frank Harary
Affiliation:
Department of MathematicsUniversity of MichiganAnn Arbor, MI 48109
Jerald A. Kabell
Affiliation:
Department of MathematicsUniversity of MichiganAnn Arbor, MI 48109
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A graph in which each line is designated as either positive or negative is called a signed graph S. The sign of a cycle in S is a product of the signs of its lines. A signed graph in which every cycle is positive is called balanced. This concept was introduced by Harary in (3) and the following characterisation of balanced signed graphs was given.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 2 , June 1981 , pp. 99 - 104
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

REFERENCES

(1)Beineke, L. W. and Harary, F., Consistent graphs with signed points, Rivista di matematica per le scienze economiche e sociale 1 (1978), 81–88.Google Scholar
(2)Cartwright, D. and Harary, F., Structural balance: A generalization of Heider's theory, Psychol. Review 63 (1956), 277–293.CrossRefGoogle ScholarPubMed
(3)Harary, F., On the notion of balance of a signed graph, Michigan Math. J. 2 (1953), 143–146.CrossRefGoogle Scholar
(4)Harary, F., The number of linear, directed, rooted, and connected graphs, Trans. Amer. Math. Soc. 78 (1955), 455–463.CrossRefGoogle Scholar
(5) F. Harary and Palmer, E. M., On the number of balanced signed graphs, Bull. Math. Biophysics 29 (1967), 759–765.Google Scholar
(6)Harary, F. and Palmer, E. M., Graphical Enumeration (Academic Press, New York, 1973).Google Scholar
(7)Harary, F., Palmer, E. M., Robinson, R. W. and Schwenk, A. J., Enumeration of graphs with signed points and lines, J. Graph Theory 1 (1977), 295–308.CrossRefGoogle Scholar