Spectra of regular graphs and hypergraphs and orthogonal polynomials

European Journal of Combinatorics

Volumn 17, Issue 5, 1996, Pages 461-477

  Li, Wen Ch'ing Winnie ^a   Solé, Patrick ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21344435017     PISSN: 01956698     EISSN: None     Source Type: Journal    
DOI: 10.1006/eujc.1996.0040     Document Type: Article

References (26)

1. E. Bannai, On the weight distribution of spherical t-designs, Europ. J. Combin., 1 (1980), 19-26.
2. C. Berge, Hypergraphes, Gauthier-Villars, Paris, 1987.
3. N. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge, 1974.
4. A. E. Brouwer, A. M. Cohen and A. Neumaier, Distance-regular graphs, Springer-Verlag, Berlin, 1989.
5. D. M. Cvetković, M. Doob and H. Sachs, Spectra of Graphs, Academic Press, London, 1979.
6. F. R. K. Chung, Diameters and eigenvalues, J. Am. Math. Soc., 2(2) (1989), 187-196.
7. C. Delorme and P. Solé, Diameter, covering number, covering radius, and eigenvalues, Europ. J. Combin., 12 (1991), 95-108.
8. K. Feng and W.-C. W. Li, Spectra of hypergraphs and applications, J. of Number Theory, to appear.
9. J. Friedman, On the second eigenvalue and random walks in random regular d-graphs, Technical Report CS-TR-172-88, Princeton University, 1988.
10. C. D. Godsil and B. Mohar, Walk generating functions and spectral measures of infinite graphs, Lin. Alg. Applics, 107 (1988), 191-206.
11. K. Hashimoto, Zeta functions of finite graphs and representations of p-adic groups. In: Automorphic Forms and Geometry of Arithmetic Varieties, K. Hashimoto and Y. Namikawa (eds), Advanced Studies In Pure Mathematics 15, Academic Press, New York (1989), pp. 211-280.
12. W. Kuich and N. Sauer, On the existence of certain minimial regular n-systems with given girth, In: Proofs and Techniques in Graph Theory, F. Harary (ed.), Academic Press, New York, 1963, pp. 93-101.
13. V. I. Levenshtein, Designs as maximal codes in polynomial metric spaces, Acta Appl. Math., 29 (1992), 1-82.
14. W.-C. W. Li, A survey of Ramanujan graphs, Proceedings of AGCT-4, Luminy 93, Arithmetic, Geometry and Coding Theory, R. Pellikaan, M. Perret, S. Vladut, eds, de Gruyter (1996).
15. W.-C. W. Li, Number-theoretic constructions of Ramanujan graphs, Astéristique, (1995), Columbia University Number Theory Seminar, NY 1992, Astérisque, 228 (1995), SMF, 101-120.
16. W.-C. W. Li, Number-theoretic constructions of Ramanujan graphs, Astéristique, (1995), Columbia University Number Theory Seminar, NY 1992, Astérisque, 228 (1995), SMF, 101-120.
17. R. A. Liebler, Tactical configurations and their generic ring, Europ. J. Combin., 9 (1988), 581-592.
18. A. Lubotzky, R. Phillips and P. Sarnak, Ramanujan graphs, Combinatorica, 8 (1988), 261-277.
19. B. D. McKay, The expected eigenvalue distribution of a large regular graph, Lin. Alg. Applies, 40 (1981), 203-216.
20. B. Mohar and W. Woess, A survey on spectra of infinite graphs, Bull. Lond. Math. Soc., 21 (1989), 209-234.
21. P. Solé, The second eigenvalue of regular graphs of given girth, J. Combin. Theory, Ser. B., 56(2) (1992), 239-249.
22. P. Solé, Packing radius, covering radius, and dual distance, IEEE Trans. Inform. Theory, 41 (1995), 268-272.
23. D. Stanton, Generalized n-gons and Chebychev polynomials, J. Combin. Theory, Ser. A, 34 (1983), 15-27.
24. T. J. Stieltjes, Recherches sur les fractions continues, Oeuvres Complètes, vol. 2, pp. 405-566, Ann. Fac. Sci. Toulouse, 9 (1894), 1-47.
25. T. J. Stieltjes, Recherches sur les fractions continues, Oeuvres Complètes, vol. 2, pp. 405-566, Ann. Fac. Sci. Toulouse, 9 (1894), 1-47.
26. G. Szegö, Orthogonal Polynomials, AMS Colloquium Publications 23, fourth edition, 1975, reprinted 1985.