Reconstructing a Generalized Quadrangle from its Distance Two Association Scheme
Sylvia A. Hobart
and Stanley E. Payne
DOI: 10.1023/A:1022451615562
Abstract
Payne [4] constructed an association scheme from a generalized quadrangle with a quasiregular point. We show that an association scheme with appropriate parameters and satisfying an assumption about maximal cliques must be one of these schemes arising from a generalized quadrangle.
Pages: 261–266
Keywords: association scheme; generalized quadrangle; quasiregular point
Full Text: PDF
References
1. A.E. Brouwer and W.H. Haemers, "Structure and uniqueness of the (81, 20, l, 6) strongly regular graph," Discrete Math. 106/107 (1992), 77-82.
2. W.H. Haemers, Eigenvalue techniques in design and graph theory, Math. Centr. Tract 121, Amsterdam, 1980.
3. A.A. Ivanov and S.V. Shpectorov, "Characterization of the association schemes of the Hermitian forms," J. Math. Soc. Japan 43 (1991), 25-48.
4. S.E. Payne, "Coherent configurations derived from quasiregular points in generalized quadrangles," to appear in the proceedings of Finite Geometry and Combinatorics, Second International Conference at Deinze, Belgium, 1992.
5. S.E. Payne and J.A. Thas, Finite Generalized Quadrangles, Pitman, New York (1985).
2. W.H. Haemers, Eigenvalue techniques in design and graph theory, Math. Centr. Tract 121, Amsterdam, 1980.
3. A.A. Ivanov and S.V. Shpectorov, "Characterization of the association schemes of the Hermitian forms," J. Math. Soc. Japan 43 (1991), 25-48.
4. S.E. Payne, "Coherent configurations derived from quasiregular points in generalized quadrangles," to appear in the proceedings of Finite Geometry and Combinatorics, Second International Conference at Deinze, Belgium, 1992.
5. S.E. Payne and J.A. Thas, Finite Generalized Quadrangles, Pitman, New York (1985).