Existence and Explicit Constructions of q + 1 Regular Ramanujan Graphs for Every Prime Power q

Journal of Combinatorial Theory, Series B

Volumn 62, Issue 1, 1994, Pages 44-62

  Morgenstern, Moshe ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002622843     PISSN: 00958956     EISSN: 10960902     Source Type: Journal    
DOI: 10.1006/jctb.1994.1054     Document Type: Article

References (26)

1. N. Alon, Eigenvalues and expanders, Combinatorica 6, No. 2 (1986), 83-96.
2. A. A. Albert, “Structure of Algebras, ” Amer. Math. Soc., New York, 1939; revised, 1961.
3. 1isoperimetric inequalities for graphs, and superconcentrations, J. Combin. Theory Ser. B 38 (1985), 73-88.
4. n, x], II, Duke Math. J. 14 (1947), 543-557.
5. L. E. Dickson, “Algebras and Their Arithmetics, ” Univ. of Chicago Press, Chicago, 1923.
6. V. G. Drjnfeld, The proof of Peterson’s conjecture for GL(2) over global field of characteristic p, Functional Anal. Appl. 22 (1988), 28-43.
7. S. Gelbart, “Automorphic Forms on Adele Groups, ” Princeton Univ. Press, Princeton, NJ, 1975.
8. O. Gaber and Z. Galil, Explicit construction of linear sized superconcentrators, J. Comput. System Sci. 22 (1981), 407-420.
9. I. M. Gelfand, M. I. Graev, and I. I. Pyatetskii-Shapiro, “Representation Theory and Automorphic Functions, ” Saunders, Philadelphia, 1969.
10. A. J. Hoffman, On eigenvalues and coloring of graphs, in “Graph Theory and its Applications” (B. Harris, Ed.), pp. 79-91, Academic Press, New York, 1970.
11. M. Klawe, Limitations on explicit constructions of expanding graphs, SIAM J. Comput. 13 (1984), 155-156.
12. 2(R), ” Springer-Verlag, New-York, 1985.
13. A. Lubotzky, R. Phillips, and P. Sarnak, Ramanujan graphs, Combinatorica 8, No. 3 (1988), 261-277.
14. A. Lubotzky, Discrete groups, expanding graphs and invariant measures, Birkhauser Progress in Math., to appear.
15. G. A. Margulis, Explicit construction of concentrators, Problems Inform. Transmission 11 (1975), 325-332.
16. G. A. Margulis, Explicit group theoretical constructions of combinatorial schemes and their application to the design of expanders and superconcentrators, Problems Inform. Transmission 24 (1988), 39-46.
17. M. Morgenstern, “Ramanujan Diagrams and Explicit Construction of Expanding Graphs, ” Ph.D. thesis, Hebrew University of Jerusalem, 1990.
18. M. S. Pinsker, On the complexity of a concentrator, in “Proceedings, 7th International Teletraffic Conf. Stockholm, 1973.”.
19. N. Pippenger, Superconcentrators, SIAM J. Comput. 6 (1972), 298-304.
20. G. Prasad, Strong approximation for semi-simple groups over function fields, Ann. of Math. 105 (1977).
21. I. Reiner, “Maximal Orders, ” Academic Press, New York, 1975.
22. J. P. Serre, “Trees, ” Springer-Verlag, New York/Berlin, 1980.
23. V. Shoup, New algorithms for finding irreducible polynomials over finite fields, in “29th Annual Symposium on Foundations of Computer Science, 1988, ” pp. 283-290.
24. L. Tornheim, Integral sets of quaternion algebras over function fields, Trans. Amer. Math. Soc. 48 (1940), 436-450.
25. M. F. Vigneras, “Arithmetique des Algebres de Quaternions, ” Lecture Notes in Math., Vol. 800, Springer-Verlag, New York/Berlin, 1980.
26. A. Weil, “Basic Number Theory, ” Springer-Verlag, New York/Berlin, 1967.