Skip to main content
SpringerLink
Log in

On the number of balanced signed graphs

  • Published:
The bulletin of mathematical biophysics Aims and scope Submit manuscript

Abstract

The classical enumeration theorem of Pólya (Acta Math.,68, 145–254, 1937) is applied to a modified version of Harary’s (Pacific J. Math.,8, 743–755, 1958) generating functions for counting bicolored graphs to derive a counting function for the number of balanced signed graphs. Methods for computing these counting polynomial functions are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Cartwright, D. and T. Gleason. 1966. “The Number of Paths and Cycles in Digraph.”Psychometrika,31, 179–199.

    Article  MATH  MathSciNet  Google Scholar 

  • — and F. Harary. 1956. “Structural Balance: A Generalization of Heider’s Theory.”Psychol. Review,63, 277–293.

    Article  Google Scholar 

  • Cartwright, D. and F. Harary. 1968. “On Colorings of Signed Graphs.”Elemente der Math.,23, to appear.

  • Davis, J. A. 1967. “Clustering and Structural Balance in Graphs.”Human Relations,20, 181–187.

    Article  Google Scholar 

  • Davis, R. L. 1954. “Structure of Dominance Relations.”Bull. Math. Biophysics,16, 131–140.

    Google Scholar 

  • Harary, F. 1953–54. “On the Notion of Balance of a Signed Graph.”Mich. Math. J.,2, 143–146.

    Article  Google Scholar 

  • — 1955. “The Number of Linear, Directed, Rooted, and Connected Graphs.”Trans. Amer. Math. Soc.,78, 445–463.

    Article  MATH  MathSciNet  Google Scholar 

  • — 1958. “On the Number of Bicolored Graphs.”Pacific J. Math.,8, 743–755.

    MATH  MathSciNet  Google Scholar 

  • — 1960. “Unsolved Problems in the Enumeration of Graphs.”Publ. Math. Inst. Hung. Acad. Sci.,5, 63–95.

    MATH  Google Scholar 

  • — 1964a. “Combinatorial Problems in Graphical Enumeration.” InApplied Combinatorial Mathematics, E. F. Beckenbach, Ed. New York: Wiley, 185–217.

    Google Scholar 

  • — 1964b. “A Graph Theoretic Approach to Similarity Relations.”Psychometrika,29, 143–151.

    Article  MATH  MathSciNet  Google Scholar 

  • — 1967.A Seminar on Graph Theory. New York: Holt, Rinehart and Winston.

    MATH  Google Scholar 

  • —, R. Norman and D. Cartwright. 1965.Structural Models: An Introduction to the Theory of Directed Graphs. New York: Wiley.

    MATH  Google Scholar 

  • — and E. M. Palmer. 1965. “The Power Group of Two Permutation Groups.”Proc. Nat. Acad. Sci. U.S.A.,54, 680–682.

    Article  MATH  MathSciNet  Google Scholar 

  • —. 1966a. “The Power Group Enumeration Theorem.”J. Combinatorial Theory,1, 157–173.

    MATH  MathSciNet  Google Scholar 

  • —. 1966b. “Enumeration of Self-Converse Digraphs.”Mathematika,13, 151–157.

    Article  MATH  MathSciNet  Google Scholar 

  • — and G. Prins. 1963. “Enumeration of Bicolourable Graphs.”Canad. J. Math.,15, 237–248.

    MATH  MathSciNet  Google Scholar 

  • — and R. C. Read. 1966. “The Probability of a Given 1-choice Structure.”Psychometrika,31, 271–278.

    Article  Google Scholar 

  • — and J. C. Ross. 1952. “On the Determination of Redundancies in Sociometric Chains.”Psychometrika,17, 195–208.

    Article  MATH  Google Scholar 

  • Moon, J. W. 1963. “A Note on ‘Pattern Variance on a Square Field’.”Psychometrika,28, 93–95.

    Article  MATH  MathSciNet  Google Scholar 

  • Parthasarathy, K. R. 1964. “Enumeration of Paths in Digraphs.”Psychometrika,29, 153–165.

    Article  MATH  MathSciNet  Google Scholar 

  • Pólya, G. 1937. “Kombinatorische Anzahlbestimmungen für Gruppen, Graphen, und chemische Verbindungen.”Acta Math.,68, 145–254.

    MATH  Google Scholar 

  • Robinson, R. W. 1968. “Enumeration of Colored Graphs.”J. Combinatorial Theory,4, to appear.

Download references

Author information

Authors and Affiliations

  1. The London School of Economics and Political Science, University College, University of London, London, England

    Frank Harary & Edgar M. Palmer

Authors
  1. Frank Harary
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edgar M. Palmer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Harary, F., Palmer, E.M. On the number of balanced signed graphs. Bulletin of Mathematical Biophysics 29, 759–765 (1967). https://doi.org/10.1007/BF02476926

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02476926

Keywords

Search

Navigation