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.
Similar content being viewed by others
References
A. E. Brouwer, A. M. Cohen and A. Neumaier, Distance-Regular Graphs, Springer-Verlag, Berlin (1989).
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).
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.
F. C. Bussemaker, R. Mathon and J. J. Seidel, Tables of two-graphs, Report 79-WSK-05, Technical University Eindhoven (1979).
D. M. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs-Theory and Application, VEB Deutscher Verlag der Wissenschaften, Berlin (1980).
E. R. van Dam, Regular graphs with four eigenvalues, Linear Algebra Appl., Vol. 226–228 (1995) pp. 139–162.
E. R. van Dam, Three-class association schemes, J. Alg. Combin., Vol. 10 (1999) pp. 69–107.
W. H. Haemers, Eigenvalue techniques in design and graph theory, Mathematical Centre Tract 121, Mathematical Centre, Amsterdam (1980).
W. H. Haemers, Interlacing eigenvalues and graphs, Linear Algebra Appl.,Vol. 226–228 (1995) pp. 593–616.
W. H. Haemers and Vladimir D. Tonchev, Spreads in strongly regular graphs, Designs, Codes and Cryptography, Vol. 8 (1996) pp. 145–157.
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.
B. McKay and E. Spence, private communication.
E. Spence, Regular two-graphs on 36 vertices, Linear Algebra Appl., Vol. 226–228 (1995) pp. 459–497.
Author information
Authors and Affiliations
Rights 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
Issue Date:
DOI: https://doi.org/10.1023/A:1008379409579