The Distance-Regular Graphs of Valency Four

Journal of Algebraic Combinatorics

Volumn 10, Issue 1, 1999, Pages 5-24

  Brouwer, A E ^a   Koolen, J H ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Distance regular graph

Indexed keywords

EID: 0038749040     PISSN: 09259899     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1018693118268     Document Type: Article

References (21)

1. E. Bannai and T. Ito, Algebraic Combinatorics I: Association Schemes, Benjamin-Cummings Lecture Note Ser. 58, Benjamin/Cummings, London, 1984.
2. E. Bannai and T. Ito, "On distance-regular graphs with fixed valency, II," Graphs and Combinatorics 4 (1988), 219-228.
3. E. Bannai and T. Ito, "On distance-regular graphs with fixed valency, III," J. Algebra 107 (1987), 43-52.
4. E. Bannai and T. Ito, "On distance-regular graphs with fixed valency, IV," Eur. J. Combin. 10 (1989), 137-148.
5. N.L. Biggs, Algebraic graph theory, Cambridge Tracts in Math., Vol. 67, Cambridge Univ. Press, 1974.
6. N.L. Biggs, A.G. Boshier, and J. Shawe-Taylor, "Cubic distance-regular graphs," J. London Math. Soc. 33(2) (1986), 385-394.
7. A. Boshier and K. Nomura, "A remark on the intersection arrays of distance-regular graphs," J. Comb. Th. (B) 44 (1988), 147-153.
8. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer, Heidelberg, 1989.
9. A.M. Cohen and J. Tits, "On generalized hexagons and a near octagon whose lines have three points," Eur. J. Combin. 6 (1985), 13-27.
10. A. Hiraki, "An improvement of the Boshier-Nomura bound," J. Combin. Th. (B) 61 (1994), 1-4.
11. A. Hiraki, "A Constant Bound for the Number of Columns (1, k - 2, 1) in the Intersection Array of Distance-Regular Graph," Graphs and Combinatorics 12 (1996), 23-37.
12. L. Kronecker, "Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten," Crelle, Journal f. d. reine u. angew. Math. 53 (1857), 173-175. Also found in Leopold Kronecker's Werke, K. Hensel (Ed.), Chelsea reprint, 1968, pp. 105-108.
13. L. Kronecker, "Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten," Crelle, Journal f. d. reine u. angew. Math. 53 (1857), 173-175. Also found in Leopold Kronecker's Werke, K. Hensel (Ed.), Chelsea reprint, 1968, pp. 105-108.
14. 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.
15. K. Nomura, "Distance-regular graphs with valency four and girth three," preprint.
16. K. Nomura, email communication, 16 May 1992.
17. K. Nomura, "A remark on bipartite distance-regular graphs of even valency," Graphs and Combinatorics 11 (1995), 139-140.
18. I. Schur, "Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahlichen Koeffizienten," Math. Zeitschrift 1 (1918), 377-402. Also found in Issai Schur, Gesammelte Abhandlungen, Alfred Brauer and Hans Rohrbach (Eds.), Springer, Berlin, 1973, Band 2, pp. 213-238.
19. I. Schur, "Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahlichen Koeffizienten," Math. Zeitschrift 1 (1918), 377-402. Also found in Issai Schur, Gesammelte Abhandlungen, Alfred Brauer and Hans Rohrbach (Eds.), Springer, Berlin, 1973, Band 2, pp. 213-238.
20. H. Suzuki, "On Distance-Biregular Graphs of Girth Divisible by Four," preprint.
21. P. Terwilliger, "Eigenvalue multiplicities of highly symmetric graphs," Discrete Math. 41 (1982), 295-302.