%0 Journal Article %1 cioaba06 %A Cioaba, Sebastian M. %D 2006 %J Linear Algebra and its Applications %K alon-boppana eigenvalues graph.theory ramanujan serre spectral_graph_theory %N 2 %P 776--782 %R 10.1016/j.laa.2005.12.020 %T Eigenvalues of Graphs and a Simple Proof of a Theorem of Greenberg %V 416 %X In his Ph.D. thesis, Greenberg proved that if ρ(X∼) is the spectral radius of the universal cover X∼ of a finite graph X, then for each ϵ>0, a positive proportion (depending only on X∼ and ϵ) of the eigenvalues of X have absolute value at least ρ(X∼)-ϵ. In this paper, we show that the same result holds true if we remove absolute from the previous result. We also prove an analogue result for the smallest eigenvalues of X.

@article{cioaba06, abstract = {In his Ph.D. thesis, Greenberg proved that if ρ(X∼) is the spectral radius of the universal cover X∼ of a finite graph X, then for each ϵ>0, a positive proportion (depending only on X∼ and ϵ) of the eigenvalues of X have absolute value at least ρ(X∼)-ϵ. In this paper, we show that the same result holds true if we remove absolute from the previous result. We also prove an analogue result for the smallest eigenvalues of X.}, added-at = {2016-10-29T16:36:07.000+0200}, author = {Cioab\u{a}, Sebastian M.}, biburl = {https://www.bibsonomy.org/bibtex/206356dc9eda1ae36f8a9275de93db99a/ytyoun}, doi = {10.1016/j.laa.2005.12.020}, interhash = {93350297c67e9ff17ae460fdc6918f53}, intrahash = {06356dc9eda1ae36f8a9275de93db99a}, issn = {0024-3795}, journal = {Linear Algebra and its Applications}, keywords = {alon-boppana eigenvalues graph.theory ramanujan serre spectral_graph_theory}, number = 2, pages = {776--782}, timestamp = {2017-02-24T09:49:27.000+0100}, title = {Eigenvalues of Graphs and a Simple Proof of a Theorem of {Greenberg}}, volume = 416, year = 2006 }