On graphs with three eigenvalues

Discrete Mathematics

Volumn 189, Issue 1-3, 1998, Pages 191-207

  Muzychuk, Mikhail ^a   Klin, Mikhail ^b  

^a BAR ILAN UNIVERSITY   (Israel)

^b BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042284276     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(98)00084-3     Document Type: Article

References (30)

1. R.W. Ahrens, G. Szekeres, On a combinatorial generalizations of the 27 lines associated with a cubic surface, J. Austral. Math.Soc. 10 (1969) 485-492.
2. E. Bannai, T. Ito, Algebraic Combinatorics. I. Association Schemes, Benjamin/Cummings, Menlo Park, 1984.
3. N. Biggs, Algebraic Graph Theory, 2nd ed., Cambridge University Press, Cambridge, 1993.
4. W.G. Bridges, R.A. Mena, Multiplicative designs II: uniform normal and reducible cases, J. Combin. Theory. A27 (1979) 269-281.
5. W.G. Bridges, R.A. Mena, Multiplicative cones - a family of three eigenvalue graphs, Aequationes. Math. 22 (1981) 208-214.
6. F.C. Bussemaker, D.M. Cvetković, J.J. Seidel, Graphs related to exceptional root systems, T.-H.-Report 76-WSK-05, Technological University, Eindhoven, 1976.
7. F.C. Bussemaker, A. Neumaier, Exceptional graphs with smallest eigenvalue -2 and related problems, Math. Comput. 59 (1992) 583-608.
8. P. Cameron (Ed.), Problems from the Fifteenth British Combinatorial Conference, Discrete Math. 167/168 (1997) 605-615.
9. P.J. Cameron, J.M. Goethals, J.J. Seidel, E.E. Shult, Line graphs, root systems and elliptic geometry, J. Algebra 43 (1976) 305-327.
10. S. Chang, The uniqueness and nonuniqueness of the triangular association scheme, Sci. Rec. 3 (1959) 604-613.
11. E. van Dam, Private Communication, January 1996.
12. E. van Dam, Private Communication, July 1996.
13. E. van Dam, Graphs with few eigenvalues - an interplay between combinatorics and algebra, CentER dissertation series 20, Thesis, Tilburg University, 1996.
14. E. van Dam, Nonregular graphs with three eigenvalues, Research Memorandum FEW 746, Tilburg University, 1997.
15. A.M. Duval, A directed version of strongly regular graphs, J. Combin. Theory A47 (1988) 71-100.
16. I.A. Faradžev, M.H. Klin, M.E. Muzichuk, Cellular rings and groups of automorphisms of graphs, in: I.A. Faradžev, A.A. Ivanov, M.H. Klin, A.J. Woldar (Eds.), Investigations in Algebraic Theory of Combinatorial Objects, Kluwer Acad. Publ., Dordrect, 1994, pp. 1-152.
17. A. Gewirtz, The uniqueness of a G(2, 2, 10, 56), Trans. New York Acad. Sci. 31 (1969) 656-675.
18. C.D. Godsil, Algebraic Combinatorics, Chapman & Hall, London, 1993.
19. C.D. Godsil, B.D. McKay, Constructing cospectral graphs, Aequationes. Math. 25 (1982) 257-268.
20. W.H. Haemers, Private Communication, October 1995.
21. W.H. Haemers, D.G. Higman, Strongly regular graphs with strongly regular decomposition, Linear Algebra Appl. 114/115 (1989) 379-398.
22. D.G. Higman, Coherent configurations I, Rend. Sem. Mat. Univ. Padova 44 (1970) 1-24.
23. D.G. Higman, Coherent algebras, Linear Algebra. Appl. 93 (1987) 209-239.
24. A.J. Hoffman, On graphs whose least eigenvalue exceeds -1 - √2, Linear Algebra Appl. 16 (1977) 153-166.
25. X. Hubant, Strongly regular graphs, Discrete Math. 13 (1975) 357-381.
26. M. Klin, A. Munemasa, M. Muzychuk, P.-H. Zischang, Directed strongly regular graphs via coherent (cellular) algebras, Kyushu-MPS-1997-12, Kyushu University, Fukuoka, Japan, June 1997.
27. J.H. van Lint, R.M. Wilson, A Course in Combinatorics, Cambridge University Press, Cambridge, 1992.
28. 2n-1(4n - 1), Acta Appl. Math. 29 (1992) 129-138.
29. J.J. Seidel, Strongly regular graphs, in: Surveys in Combinatorics, London Math. Soc. Lect. Notes Ser vol. 38, (1979), pp. 157-180.
30. B. Weisfeiler (Ed.), On construction and identification of graphs, Lecture Notes in Math., vol. 558 Berlin, Springer, 1976.