Skip to main content
SpringerLink
Log in

The spectral geometry ofk-regular graphs

  • Published:
Journal d’Analyse Mathématique Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. N. Alon,Eigenvalues and expanders, Combinatorica6 (1986), 83–96.

    Article  MATH  MathSciNet  Google Scholar 

  2. L. Babai, W. M. Kantor and A. Lubotzky,Small diameter Cayley graphs for finite simple groups, European J. Comb.10 (1989), 507–522.

    MATH  MathSciNet  Google Scholar 

  3. H. Bass,The Ihara-Selberg zeta function of a tree lattive, preprint.

  4. R. Brooks,Combinatorial problems in spectral geometry, inCurvature and Topology of Riemannian Manifolds, Springer Lecture Notes120 (1987), 14–32.

    Google Scholar 

  5. R. Brooks,Injectivity radius and low eigenvalues of hyperbolic manifolds, J. Reine Angew. Math.390 (1988), 117–129.

    MATH  MathSciNet  Google Scholar 

  6. R. Brooks,The spectral geometry of a tower of coverings, J. Differ. Geom.23 (1980), 97–107.

    MathSciNet  Google Scholar 

  7. M. W. Buck,Expanders and diffusers, SIAM J. Alg. Disc. Math.7 (1986), 282–304.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. Burger,Cheng’s inequality for graphs, preprint

  9. P. Cartier,Géometrie et Analyse sur les Arbres, Sem. Bourbaki no. 407, Springer Lecture Notes 317.

  10. P. Cartier,Harmonic analysis on trees, in Harmonic Analysis on Homogeneous Spaces (C. Moore, ed.), Proc. Symp. Pure Math. XXVI, 1973, pp. 419–424.

    MathSciNet  Google Scholar 

  11. S. Y. Cheng,Eigenvalue comparison theorems and its geometric applications, Math. Z.143 (1975), 289–297.

    Article  MATH  MathSciNet  Google Scholar 

  12. F. R. K. Chung,Diameters and eigenvalues, J. Am. Math. Soc.2 (1989), 187–196.

    Article  MATH  Google Scholar 

  13. H. Davenport,On certain exponential sums, J. für Math.169 (1933), 158–176.

    Google Scholar 

  14. A. Figa-Talamanca and C. Nebia,Harmonic Analysis and Representation Theory for Groups Acting on Homogeneous Trees, Lecture notes.

  15. K. I. Hasimoto,On zeta and L-functions on finite graphs, Int. J. Math.1 (1990), 381–396.

    Article  Google Scholar 

  16. P. Lax and R. Phillips,The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces, J. Funct. Anal.46 (1982), 280–350.

    Article  MATH  MathSciNet  Google Scholar 

  17. A. Lubotzky,Discrete Groups, Expanding Graphs, and Invariant Measures, CBMS Lecture Notes, to appear.

  18. A. Lubotzky and S. Mozes,Howe-Moore property of automorphism groups of trees, preprint.

  19. A. Lubotzky, R. Phillips and P. Sarnak,Ramanujan graphs, Combinatorica8(3) (1988), 261–277.

    Article  MATH  MathSciNet  Google Scholar 

  20. A. Pizer,Ramanujan graphs and Hecke operators, Bull. Am. Math. Soc. 23 (1990), 127–137.

    Article  MATH  MathSciNet  Google Scholar 

  21. P. Sarnak,Some Applications of Modular Forms, Cambridge University Press, 1990.

  22. T. Sunada,Fundamental groups and Laplacians, inGeometry and Analysis on Manifolds (T. Sunada, ed.), Springer Lecture Notes1339 (1988), 248–277.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Southern California, 90089-1113, Los Angeles, CA, USA

    Robert Brooks

Authors
  1. Robert Brooks
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Partially supported by N.S.F. grants DMS-8801158 and 9000631.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brooks, R. The spectral geometry ofk-regular graphs. J. Anal. Math. 57, 120–151 (1991). https://doi.org/10.1007/BF03041067

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03041067

Keywords

Search

Navigation