Eigenvalues of Graphs and Sobolev Inequalities
- 1 March 1995
- journal article
- research article
- Published by Cambridge University Press (CUP) in Combinatorics, Probability and Computing
- Vol. 4 (1) , 11-25
- https://doi.org/10.1017/s0963548300001449
Abstract
We derive bounds for eigenvalues of the Laplacian of graphs using discrete versions of the Sobolev inequalities and heat kernel estimates.Keywords
This publication has 11 references indexed in Scilit:
- Spectral Graph TheoryCBMS Regional Conference Series in Mathematics, 1996
- Local Expansion of Symmetrical GraphsCombinatorics, Probability and Computing, 1992
- Isoperimetric numbers of graphsJournal of Combinatorial Theory, Series B, 1989
- Ramanujan graphsCombinatorica, 1988
- Spectral and function theory for combinatorial LaplaciansContemporary Mathematics, 1988
- Isoperimetric inequalities and Markov chainsJournal of Functional Analysis, 1985
- λ1, Isoperimetric inequalities for graphs, and superconcentratorsJournal of Combinatorial Theory, Series B, 1985
- Groups of polynomial growth and expanding mapsPublications mathématiques de l'IHÉS, 1981
- Estimates of eigenvalues of a compact Riemannian manifoldPublished by American Mathematical Society (AMS) ,1980
- On the Eigenvalues of Vibrating Membranes†Proceedings of the London Mathematical Society, 1961