Skip to main content
Log in

The Search for Pseudo Orthogonal Latin Squares of Order Six

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

We report on the completecomputer search for a strongly regular graph with parameters(36,15,6,6) and chromatic number six. The resultis that no such graph exists.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. E. Brouwer, A. M. Cohen and A. Neumaier, Distance-Regular Graphs, Springer-Verlag, Berlin (1989).

    Google Scholar 

  2. F. C. Bussemaker, S. Cobeljic, D. M. Cvetkovic and J. J. Seidel, Computer investigations of cubic graphs, Report 76-WSK-01, Technical University Eindhoven (1976).

  3. F. C. Bussemaker, W. H. Haemers, R. Mathon and H. A. Wilbrink, A (49, 16, 3, 6) strongly regular graph does not exist, Europ. J. Combinatorics, Vol. 10 (1989) pp. 413–418.

    Google Scholar 

  4. F. C. Bussemaker, R. Mathon and J. J. Seidel, Tables of two-graphs, Report 79-WSK-05, Technical University Eindhoven (1979).

  5. D. M. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs-Theory and Application, VEB Deutscher Verlag der Wissenschaften, Berlin (1980).

    Google Scholar 

  6. E. R. van Dam, Regular graphs with four eigenvalues, Linear Algebra Appl., Vol. 226–228 (1995) pp. 139–162.

    Google Scholar 

  7. E. R. van Dam, Three-class association schemes, J. Alg. Combin., Vol. 10 (1999) pp. 69–107.

    Google Scholar 

  8. W. H. Haemers, Eigenvalue techniques in design and graph theory, Mathematical Centre Tract 121, Mathematical Centre, Amsterdam (1980).

    Google Scholar 

  9. W. H. Haemers, Interlacing eigenvalues and graphs, Linear Algebra Appl.,Vol. 226–228 (1995) pp. 593–616.

    Google Scholar 

  10. W. H. Haemers and Vladimir D. Tonchev, Spreads in strongly regular graphs, Designs, Codes and Cryptography, Vol. 8 (1996) pp. 145–157.

    Google Scholar 

  11. A. J. Hoffman, On eigenvalues and colourings of graphs, Graph Theory and Its Applications (B. Harris, ed.), Academic Press, New York (1970) pp. 79–91.

    Google Scholar 

  12. B. McKay and E. Spence, private communication.

  13. E. Spence, Regular two-graphs on 36 vertices, Linear Algebra Appl., Vol. 226–228 (1995) pp. 459–497.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bussemaker, F.C., Haemers, W.H. & Spence, E. The Search for Pseudo Orthogonal Latin Squares of Order Six. Designs, Codes and Cryptography 21, 77–82 (2000). https://doi.org/10.1023/A:1008379409579

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008379409579

Navigation