Eigenvalue ratios of nonnegatively curved graphs
Spectral Theory
2019-04-03 v2 Combinatorics
Abstract
We derive an optimal eigenvalue ratio estimate for finite weighted graphs satisfying the curvature-dimension inequality . This estimate is independent of the size of the graph and provides a general method to obtain higher order spectral estimates. The operation of taking Cartesian products is shown to be an efficient way for constructing new weighted graphs satisfying . We also discuss a higher order Cheeger constant ratio estimate and related topics about expanders.
Keywords
Cite
@article{arxiv.1406.6617,
title = {Eigenvalue ratios of nonnegatively curved graphs},
author = {Shiping Liu and Norbert Peyerimhoff},
journal= {arXiv preprint arXiv:1406.6617},
year = {2019}
}