Skip to main content
SpringerLink
Log in
Book cover

Combinatorial Mathematics V pp 28–43Cite as

Counting unlabeled acyclic digraphs

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 622))

Abstract

The previously known ways to count acyclic digraphs, both labeled and unlabeled, are reviewed. Then a new method of enumerating unlabeled acyclic digraphs is developed. It involves computing the sum of the cyclic indices of the automorphism groups of the acyclic digraphs, achieving a considerable gain in efficiency through an application of the inclusion-exclusion principle. Numerical results are reported on, and a table of the numbers of unlabeled acyclic digraphs on up to 18 points is included.

The author is grateful to the Australian Research Grants Committee for providing the support necessary for the programming of all the numerical work. This was performed by Dr. Paul Butler. The running times reported were observed on a PDP-11/45 with secondary storage on an RK05 disc.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W. Burnside, Theory of Groups of Finite Order. 2nd ed., Cambridge Univ. Press, London, 1911. Reprinted by Dover, New York, 1955.

    MATH  Google Scholar 

  2. F. Harary and E.M. Palmer, Graphical Enumeration. Academic Press, New York, 1973.

    MATH  Google Scholar 

  3. C.L. Liu, Introduction to Combinatorial Mathematics. McGraw-Hill, New York, 1968.

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  5. J.H. Redfield, The theory of group reduced distributions, Amer. J. Math. 49 (1927) 433–455.

    Article  MathSciNet  MATH  Google Scholar 

  6. R.W. Robinson, Enumeration of nonseparable graphs, J. Combinatorial Theory 9 (1970) 327–356.

    Article  MathSciNet  MATH  Google Scholar 

  7. R.W. Robinson, Enumeration of acyclic digraphs, Combinatorial Mathematics and Its Applications. (R.C. Bose et al., eds) Univ. of North Carolina, Chapel Hill (1970) 391–399.

    Google Scholar 

  8. R.W. Robinson, Counting labeled acyclic digraphs, New Directions in the Theory of Graphs. (Frank Harary, ed.) Academic Press, New York (1973) 239–273.

    Google Scholar 

Download references

Authors
  1. R. W. Robinson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Charles H. C. Little

Rights and permissions

Reprints and permissions

Copyright information

© 1977 Springer-Verlag

About this paper

Cite this paper

Robinson, R.W. (1977). Counting unlabeled acyclic digraphs. In: Little, C.H.C. (eds) Combinatorial Mathematics V. Lecture Notes in Mathematics, vol 622. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069178

Download citation

  • DOI: https://doi.org/10.1007/BFb0069178

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08524-9

  • Online ISBN: 978-3-540-37020-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation