Skip to main content

Is the null-graph a pointless concept?

Part I: Invited Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 406)

Abstract

The graph with no points and no lines is discussed critically. Arguments for and against its official admittance as a graph are presented. This is accompanied by an extensive survey of the literature. Paradoxical properties of the null-graph are noted. No conclusion is reached.

Keywords

  • Label Graph
  • Enumeration Problem
  • Label Tree
  • Finite Graph
  • Chromatic Polynomial

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/BFb0066433
  • Chapter length: 8 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   84.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-37809-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   109.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berge, C., The Theory of Graphs and its Applications. Wiley, New York, 1962.

    MATH  Google Scholar 

  2. Busacker, R. and Saaty, T., Finite Graphs and Networks. McGraw-Hill, New York, 1965.

    MATH  Google Scholar 

  3. Harary, F., The Number of Linear, Directed, Rooted, and Connected Graphs. Trans. American Mathematical Society, 78 (1955), pp. 445–463.

    MATH  CrossRef  Google Scholar 

  4. Harary, F., Graph Theory. Addison-Wesley, Reading, Massachusetts, 1969.

    Google Scholar 

  5. König, D. Theorie der endlichen und unendlichen Graphen. Leipzig, 1936. Reprinted Chelsea, New York, 1950.

    Google Scholar 

  6. Maxwell, L. M., and Reed, M. B., Theory of Graphs: A Basis for Network Theory, Pergamon Press, New York, 1971.

    Google Scholar 

  7. Ore, O., Theory of Graphs. American Mathematical Society Colloq. Publ. Volume 38, Providence, 1962.

    Google Scholar 

  8. Read, R. C., An Introduction to Chromatic Polynomials. J. Combinatorial Theory 4 (1968), pp. 52–71.

    MathSciNet  CrossRef  Google Scholar 

  9. Read, R. C., A Mathematical Background for Economists and Social Scientists, Prentice-Hall, Englewood Cliffs, 1971.

    Google Scholar 

  10. Sachs, H., Einführung in die Theorie der endlichen Graphen, Teil I. Teubner, Leipzig, 1970.

    MATH  Google Scholar 

  11. Sedlaček, J., Einführung in die Graphentheorie, Teubner, Leipzig, 1968.

    MATH  Google Scholar 

  12. Tutte, W. T., The Connectivity of Graphs. Toronto University Press, Toronto, 1967.

    Google Scholar 

  13. Wagner, K., Graphentheorie, Bibliographisches Institut, Mannheim, 1970.

    MATH  Google Scholar 

  14. Zykov, A. A., Theory of Finite Graphs (Russian), Nauka, Novosibirsk, 1969.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1974 Springer-Verlag Berlin

About this paper

Cite this paper

Harary, F., Read, R.C. (1974). Is the null-graph a pointless concept?. In: Bari, R.A., Harary, F. (eds) Graphs and Combinatorics. Lecture Notes in Mathematics, vol 406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066433

Download citation

  • DOI: https://doi.org/10.1007/BFb0066433

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06854-9

  • Online ISBN: 978-3-540-37809-9

  • eBook Packages: Springer Book Archive