The Regular Near Polygons of Order ( s, 2)
Akira Hiraki
and Jack Koolen
DOI: 10.1023/B:JACO.0000047296.94830.e7
Abstract
Pages: 219–235
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. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency, II,” Graphs and Combin. 4 (1988), 219-228.
3. N.L. Biggs, Algebraic Graph Theory, Cambridge Tracts in Math, Cambridge Univ. Press, Vol. 67, 1974.
4. N.L. Biggs, A.G. Boshier, and J. Shawe-Taylor, “Cubic distance-regular graphs,” J. London Math. Soc. 33 (2) (1986), 385-394.
5. A. Boshier and K. Nomura, “A remark on the intersection arrays of distance-regular graphs,” J. of Comb. Theory, Ser. B 44 (1988), 147-153.
6. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer, Heidelberg, 1989.
7. Y. Egawa, “Characterization of H (n, q) by the parameters,” J. of Combin. Theory Ser. A 31 (1981), 108-125.
8. W. Feit and G. Higman, “The non-existence of certain generalized polygons,” J. Algebra. 1 (1964), 114-131.
9. F.J. Fuglister, “On generalized moore geometries I, II,” Discrete Math. 67 (1987), 249-269.
10. C.D. Godsil, Algebraic Combinatorics, Chapman and Hall, New York, 1993.
11. W.H. Haemers and C. Roos, “An inequality for generalized hexagons,” Geom. Dedicata 10 (1981), 219-222.
12. D.G. Higman, “Partial geometries generalized quadrangles and strongly regular graphs,” in: Atti del Convegno di Geometria, Combinatoria e sue Applicazioni (Univ. degli Studi di Perugia, Perugia, 1970), Perugia 1971, pp. 263-293.
13. D.G. Higman, “Invariant relations, coherent configurations and generalized polygons,” Combinatorics, Math Centre Tracts, Amsterdam 57 (1974), 27-43.
14. A. Hiraki, “Circuit chasing technique in a distance-regular graph with triangles,” Europ. J. Combin. 14 (1993), 413-420.
15. A. Hiraki, K. Nomura, and H. Suzuki, “Distance-regular graphs of valency 6 and a1 = 1,” J. of Alg. Combin. 11 (2000), 101-134.
16. T. Ito, “Bipartite distance-regular graphs of valency three,” Linear Algebra Appl. 46 (1982), 195-213.
17. B. Mohar and J. Shawe-Taylor, “Distance-biregular graphs with 2-valent vertices and distance-regular line graphs,” J. of Comb. Theory, Ser (B) 38 (1985), 193-203.
18. E. Shult and A. Yanushka, “Near n-gons and line systems,” Geom. Dedicata. 9 (1980), 1-76.
2. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency, II,” Graphs and Combin. 4 (1988), 219-228.
3. N.L. Biggs, Algebraic Graph Theory, Cambridge Tracts in Math, Cambridge Univ. Press, Vol. 67, 1974.
4. N.L. Biggs, A.G. Boshier, and J. Shawe-Taylor, “Cubic distance-regular graphs,” J. London Math. Soc. 33 (2) (1986), 385-394.
5. A. Boshier and K. Nomura, “A remark on the intersection arrays of distance-regular graphs,” J. of Comb. Theory, Ser. B 44 (1988), 147-153.
6. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer, Heidelberg, 1989.
7. Y. Egawa, “Characterization of H (n, q) by the parameters,” J. of Combin. Theory Ser. A 31 (1981), 108-125.
8. W. Feit and G. Higman, “The non-existence of certain generalized polygons,” J. Algebra. 1 (1964), 114-131.
9. F.J. Fuglister, “On generalized moore geometries I, II,” Discrete Math. 67 (1987), 249-269.
10. C.D. Godsil, Algebraic Combinatorics, Chapman and Hall, New York, 1993.
11. W.H. Haemers and C. Roos, “An inequality for generalized hexagons,” Geom. Dedicata 10 (1981), 219-222.
12. D.G. Higman, “Partial geometries generalized quadrangles and strongly regular graphs,” in: Atti del Convegno di Geometria, Combinatoria e sue Applicazioni (Univ. degli Studi di Perugia, Perugia, 1970), Perugia 1971, pp. 263-293.
13. D.G. Higman, “Invariant relations, coherent configurations and generalized polygons,” Combinatorics, Math Centre Tracts, Amsterdam 57 (1974), 27-43.
14. A. Hiraki, “Circuit chasing technique in a distance-regular graph with triangles,” Europ. J. Combin. 14 (1993), 413-420.
15. A. Hiraki, K. Nomura, and H. Suzuki, “Distance-regular graphs of valency 6 and a1 = 1,” J. of Alg. Combin. 11 (2000), 101-134.
16. T. Ito, “Bipartite distance-regular graphs of valency three,” Linear Algebra Appl. 46 (1982), 195-213.
17. B. Mohar and J. Shawe-Taylor, “Distance-biregular graphs with 2-valent vertices and distance-regular line graphs,” J. of Comb. Theory, Ser (B) 38 (1985), 193-203.
18. E. Shult and A. Yanushka, “Near n-gons and line systems,” Geom. Dedicata. 9 (1980), 1-76.