A Higman-Haemers Inequality for Thick Regular Near Polygons
Akira Hiraki
and Jack Koolen
DOI: 10.1023/B:JACO.0000047283.91464.3c
Abstract
In this note we will generalize the Higman-Haemers inequalities for generalized polygons to thick regular near polygons.
Pages: 213–218
Keywords: regular near polygon; distance-regular graph
Full Text: PDF
References
1. E. Bannai and T. Ito, Algebraic Combinatorics I: Association Schemes, Benjamin-Cummings Lecture Note Ser. 58, Benjamin/Cummings Publ. Co., London, 1984.
2. N.L. Biggs, Algebraic Graph Theory, Cambridge Tracts in Math. 67, Cambridge Univ. Press, 1974.
3. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer, Heidelberg, 1989.
4. A.E. Brouwer and H.A. Wilbrink, “The structure of near polygons with quads,” Geom. Dedicata 14 (1983) 145-176.
5. W. Feit and G. Higman, “The non-existence of certain generalized polygons,” J. Algebra 1 (1964), 114-131.
6. C.D. Godsil, Algebraic Combinatorics, Chapman and Hall, New York, 1993.
7. W.H. Haemers and C. Roos, “An inequality for generalized hexagons,” Geom. Dedicata 10 (1981), 219-222.
8. D.G. Higman, “Partial geometries generalized quadrangles and strongly regular graphs,” pp. 263-293 in Atti del Convegno di Geometria, Combinatoria e sue Applicazioni (Univ. degli Studi di Perugia, Perugia, 1970), Perugia 1971.
9. D.G. Higman, “Invariant relations, coherent configurations and generalized polygons,” pp. 27-43 in Combinatorics, Math Centre Tracts 57, Amsterdam, 1974.
10. A. Hiraki, “Strongly closed subgraphs in a regular thick near polygons,” European J. Combin. 20 (1999), 789-796.
11. A. Hiraki and J.H. Koolen, “An improvement of the Godsil bound,” Ann. of Combin. 6 (2002), 33-44.
12. J. Tits, “Sur la trialité et certains groups qui s'en déduisent,” Publ. Math. I.H.E.S. 2 (1959), 14-60.
2. N.L. Biggs, Algebraic Graph Theory, Cambridge Tracts in Math. 67, Cambridge Univ. Press, 1974.
3. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer, Heidelberg, 1989.
4. A.E. Brouwer and H.A. Wilbrink, “The structure of near polygons with quads,” Geom. Dedicata 14 (1983) 145-176.
5. W. Feit and G. Higman, “The non-existence of certain generalized polygons,” J. Algebra 1 (1964), 114-131.
6. C.D. Godsil, Algebraic Combinatorics, Chapman and Hall, New York, 1993.
7. W.H. Haemers and C. Roos, “An inequality for generalized hexagons,” Geom. Dedicata 10 (1981), 219-222.
8. D.G. Higman, “Partial geometries generalized quadrangles and strongly regular graphs,” pp. 263-293 in Atti del Convegno di Geometria, Combinatoria e sue Applicazioni (Univ. degli Studi di Perugia, Perugia, 1970), Perugia 1971.
9. D.G. Higman, “Invariant relations, coherent configurations and generalized polygons,” pp. 27-43 in Combinatorics, Math Centre Tracts 57, Amsterdam, 1974.
10. A. Hiraki, “Strongly closed subgraphs in a regular thick near polygons,” European J. Combin. 20 (1999), 789-796.
11. A. Hiraki and J.H. Koolen, “An improvement of the Godsil bound,” Ann. of Combin. 6 (2002), 33-44.
12. J. Tits, “Sur la trialité et certains groups qui s'en déduisent,” Publ. Math. I.H.E.S. 2 (1959), 14-60.