Distance-Regular Graphs of Valency 6 and a1 = 1
Akira Hiraki
, Kazumasa Nomura
and Hiroshi Suzuki
DOI: 10.1023/A:1008776031839
Abstract
Pages: 101–134
Keywords: distance-regular graph; association scheme; P-polynomial scheme
Full Text: PDF
References
1. E. Bannai and T. Ito, Algebraic Combinatorics I, Benjamin-Cummings, California, 1984.
2. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency,” Graphs and Combin. 3 (1987), 95-109.
3. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency,” II, Graphs and Combin. 4 (1988), 219-228.
4. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency,” IV, Europ. J. Combin. 10 (1989), 137-148.
5. N. L. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge,
1974. HIRAKI, NOMURA AND SUZUKI
6. N. L. Biggs, A. G. Boshier, and J. Shawe-Taylor, “ Cubic distance-regular graphs,” J. London Math. Soc. (2) 33 (1986), 385-394.
7. A. Boshier and K. Nomura, “A remark on the intersection arrays of distance-regular graphs,” J. Combin. Th. (B) 44 (1988), 147-153.
8. A. E. Brouwer, A. M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer Verlag, Berlin, Heidelberg, 1989.
9. A. Hiraki, “A circuit chasing technique in a distance-regular graph with triangles,” Europ. J. Combin. 14 (1993), 413-420.
10. A. Hiraki and H. Suzuki, “On distance regular graphs with b1 = cd - 1,” Mathematica Japonica 37 (1992), 751-756.
11. T. Ito, “Bipartite distance-regular graphs of valency three,” Linear Algebra Appl. 46 (1982), 195-213.
12. A. A. Ivanov, “Bounding the diameter of a distance regular graph,” Soviet Math. Dokl. 28 (1983), 149-152.
13. B. Mohar and J. Shawe-Taylor, “Distance-biregular graphs with 2-valent vertices and distance-regular line graphs,” J. Combin. Th. (B) 38 (1985), 193-203.
14. H. Suzuki, “Bounding the diameter of a distance regular graph by a function of kd ,” Graphs and Combin. 7 (1991), 363-375.
15. H. Suzuki, “Bounding the diameter of a distance regular graph by a function of kd ,” II, J. Algebra 169, (1994), 713-750.
16. N. Yamazaki, “Distance-regular graphs with (x) 3 * Ka+1,” Europ. J. Combin. 16 (1995), 525-536.
2. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency,” Graphs and Combin. 3 (1987), 95-109.
3. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency,” II, Graphs and Combin. 4 (1988), 219-228.
4. E. Bannai and T. Ito, “On distance-regular graphs with fixed valency,” IV, Europ. J. Combin. 10 (1989), 137-148.
5. N. L. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge,
1974. HIRAKI, NOMURA AND SUZUKI
6. N. L. Biggs, A. G. Boshier, and J. Shawe-Taylor, “ Cubic distance-regular graphs,” J. London Math. Soc. (2) 33 (1986), 385-394.
7. A. Boshier and K. Nomura, “A remark on the intersection arrays of distance-regular graphs,” J. Combin. Th. (B) 44 (1988), 147-153.
8. A. E. Brouwer, A. M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer Verlag, Berlin, Heidelberg, 1989.
9. A. Hiraki, “A circuit chasing technique in a distance-regular graph with triangles,” Europ. J. Combin. 14 (1993), 413-420.
10. A. Hiraki and H. Suzuki, “On distance regular graphs with b1 = cd - 1,” Mathematica Japonica 37 (1992), 751-756.
11. T. Ito, “Bipartite distance-regular graphs of valency three,” Linear Algebra Appl. 46 (1982), 195-213.
12. A. A. Ivanov, “Bounding the diameter of a distance regular graph,” Soviet Math. Dokl. 28 (1983), 149-152.
13. B. Mohar and J. Shawe-Taylor, “Distance-biregular graphs with 2-valent vertices and distance-regular line graphs,” J. Combin. Th. (B) 38 (1985), 193-203.
14. H. Suzuki, “Bounding the diameter of a distance regular graph by a function of kd ,” Graphs and Combin. 7 (1991), 363-375.
15. H. Suzuki, “Bounding the diameter of a distance regular graph by a function of kd ,” II, J. Algebra 169, (1994), 713-750.
16. N. Yamazaki, “Distance-regular graphs with (x) 3 * Ka+1,” Europ. J. Combin. 16 (1995), 525-536.