Skip to main content
SpringerLink
Log in

The number of homeomorphically irreducible trees, and other species

  • Published:
Acta Mathematica

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

References

  1. A. Cayley,Collected mathematical papers. Cambridge 1889–1897, vol. 3, 242–246 and vol. 11, 365–367.

  2. G. W. Ford &G. E. Uhlenbeck, Combinatorial problems in the theory of graphs, I, II, III and IV.Proc. Nat. Acad. Sci. U.S.A., 42 (1956), 122–128, 203–208, 529–535 and 43 (1957) 163–167. (R. Z. Norman is the third co-author of II.)

    Article  MATH  MathSciNet  Google Scholar 

  3. E. N. Gilbert, Enumeration of labelled graphs.Canadian J. Math., 8 (1956), 405–411.

    MATH  Google Scholar 

  4. F. Harary, On the notion of balance of a signed graph.Michigan Math. J., 2 (1953–1954), 143–146.

    Article  MathSciNet  Google Scholar 

  5. —, The number of linear, directed, rooted and connected graphs.Trans. Amer. Math. Soc., 78 (1955), 445–463.

    Article  MATH  MathSciNet  Google Scholar 

  6. —, Note on the Pólya and Otter formulas for enumerating trees.Michigan Math. J., 3 (1955–1956), 109–112.

    Article  MathSciNet  Google Scholar 

  7. F. Harary &R. Z. Norman, The dissimilarity characteristic of Husimi trees.Ann. of Math., 58 (1953), 134–141.

    Article  MathSciNet  Google Scholar 

  8. —, The dissimilarity characteristic of linear graphs.Proc. Amer. Math. Soc., 5 (1954), 131–135.

    Article  MATH  MathSciNet  Google Scholar 

  9. F. Harary &G. E. Uhlenbeck, On the number of Husimi trees.Proc. Nat. Acad. Sci. U.S.A., 39 (1953), 315–322.

    Article  MATH  MathSciNet  Google Scholar 

  10. D. König,Theorie der endlichen und unendlichen Graphen. Leipzig, 1936; reprinted New York, 1950.

  11. R. Z. Norman, The number of graphs with given blocks. In process of publication.

  12. R. Otter, The number of trees.Ann. of Math., 49 (1948), 583–599.

    Article  MathSciNet  Google Scholar 

  13. G. Pólya, Kombinatorische Anzahlbestimmungen für Graphen und chemische Verbindungen.Acta Math., 68 (1937), 145–254.

    Article  MATH  Google Scholar 

  14. J. Riordan, The numbers of labeled colored and chromatic trees.Acta Math., 97 (1957), 211–225.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Princeton

    Frank Harary & Geert Prins

  2. Amsterdam

    Frank Harary & Geert Prins

Authors
  1. Frank Harary
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Geert Prins
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The work of the first author was supported by grants from the National Science Foundation to the Institute for Advanced Study and from the Office of Naval Research to Princeton University, while on leave from the University of Michigan; the work of the second author was done at the University of Michigan and in Amsterdam.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Harary, F., Prins, G. The number of homeomorphically irreducible trees, and other species. Acta Math. 101, 141–162 (1959). https://doi.org/10.1007/BF02559543

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02559543

Keywords

Search

Navigation