Skip to main content
SpringerLink
Log in
Book cover

International Conference on Parallel Processing and Applied Mathematics

PPAM 2003: Parallel Processing and Applied Mathematics pp 42–49Cite as

On Generalized Moore Digraphs

  • Conference paper

  • 483 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3019))

Abstract

The transmission of a strongly connected digraph D is defined as the sum of all distances in D. A lower bound for the transmission in terms of the order n and the maximal outdegree Δ +  of D can be regarded as a generalization of the Moore bound for digraphs. Bridges and Toueg showed that Moore digraphs in the strong sense exist only for the trivial cases Δ + =1 or Δ + =n-1. Using techniques founded on Cayley digraphs, we constructed vertex-symmetric generalized Moore digraphs. Such graphs are applicable to interconnection networks of parallel computers, routers, switches, backbones, etc.

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   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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. Besche, H.U., Eick, B.: The groups of order at most 1000 except 512 and 768. Journal of Symbolic Computation 27, 405–413 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  2. Biggs, N.: Algebraic Graph Theory, 2nd edn. Cambridge University Press, Cambridge (1993)

    Google Scholar 

  3. Bollobás, B.: Extremal Graph Theory. Academic Press, London (1978)

    MATH  Google Scholar 

  4. Bridges, W.G., Toueg, S.: On the impossibility of directed Moore graphs. Journal of Combinatorial Theory, Series B 29, 339–341 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  5. Buset, D.: Maximal cubic graphs with diameter 4. Discrete Applied Mathematics 101, 53–61 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Buskens, R.W., Rogers, M.J., Stanton, R.G.: A census of tetravalent generalized Moore networks. Congressus Numerantium 52, 255–296 (1986)

    MathSciNet  Google Scholar 

  7. Buskens, R.W., Stanton, R.G.: The generalized Moore graphs on eleven vertices. Journal of Combinatorial Mathematics and Combinatorial Computing 1, 23–66 (1987)

    MATH  MathSciNet  Google Scholar 

  8. Buskens, R.W., Stanton, R.G.: Generalized Moore graphs on twelve and thirteen vertices. Ars Combinatoria 23-B, 87–132 (1987)

    MathSciNet  Google Scholar 

  9. Cerf, V.G., Cowan, D.D., Mullin, R.C., Stanton, R.G.: Computer networks and generalized Moore graphs. Congressus Numerantium 9, 379–398 (1973)

    Google Scholar 

  10. Cerf, V.G., Cowan, D.D., Mullin, R.C., Stanton, R.G.: Trivalent generalized Moore networks on sixteen nodes. Utilitas Mathematica 6, 259–283 (1974)

    MATH  MathSciNet  Google Scholar 

  11. Cerf, V.G., Cowan, D.D., Mullin, R.C., Stanton, R.G.: A partial census of trivalent generalized Moore networks. In: Street, A.P., Wallis, W.D. (eds.) Proceedings of the 3rd Australian Conference on Combinatorial Mathematics. Lecture Notes in Mathematics, vol. 452, pp. 1–27. Springer, Berlin (1975)

    Chapter  Google Scholar 

  12. Comellas, F., Fiol, M.A.: Vertex symmetric digraphs with small diameter. Discrete Applied Mathematics 58, 1–11 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  13. Comellas, F.: The (degree, diameter) problem for graphs, http://wwwmat.upc.es/grup_de_grafs/table_g.html

  14. Hoffman, J., Singleton, R.R.: On Moore graphs with diameters 2 and 3. IBM Journal of Research and Development 4, 497–504 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  15. Lakshmivarahan, S., Jwo, J.-S., Dhall, S.K.: Symmetry in interconnection networks based on Cayley graphs of permutation groups: A survey. Parallel Computing 19, 361–407 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  16. Miller, M., Fris, I.: Maximum order digraphs for diameter 2 or degree 2. In: Rees, R.S. (ed.) Graphs, matrices, and designs. Lecture Notes in Pure and Applied Mathematics, vol. 139, pp. 269–278. Dekker, New York (1993)

    Google Scholar 

  17. Sampels, M.: Large networks with small diameter. In: Möhring, R.H. (ed.) WG 1997. LNCS, vol. 1335, pp. 288–302. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  18. Sampels, M.: Algebraic Construction of Efficient Interconnection Networks (in German: Algebraische Konstruktion effizienter Verbindungsnetzwerke). Dissertation, University of Oldenburg, Germany (1998)

    Google Scholar 

  19. Sampels, M., Vilents, M.: Symmetric interconnection networks in the design of switches for WANs and LANs. In: Baum, D., Müller, N., Rödler, R. (eds.) Proceedings of the 10th GI/ITG Special Interest Conference on Measurement, Modelling and Evaluation of Computer and Communication Systems (MMB 1999), pp. 43–48. University of Trier (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut de Recherches Interdisciplinaires et de, Développements en Intelligence Artificielle, Université Libre de Bruxelles, CP 194/6, 50, avenue Franklin D Roosevelt, 1050, Bruxelles, Belgium

    Michael Sampels

Authors
  1. Michael Sampels
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Computational and Information Sciences, Czestochowa University of Technology,  

    Roman Wyrzykowski

  2. Computer Science Department, University of Tennessee, TN 37996-3450, Knoxville, USA

    Jack Dongarra

  3. Systems Research Institute, Polish Academy of Science, Warsaw, Poland

    Marcin Paprzycki

  4. Informatics & Mathematical Modeling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Jerzy Waśniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sampels, M. (2004). On Generalized Moore Digraphs. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2003. Lecture Notes in Computer Science, vol 3019. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24669-5_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24669-5_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21946-0

  • Online ISBN: 978-3-540-24669-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation