%0 Journal Article %1 nilli12 %A Nilli, A. %D 2012 %K alon-boppana eigenvalues expander graph.theory ramanujan serre %T Tight Estimates for Eigenvalues of Regular Graphs %U http://www.combinatorics.org/ojs/index.php/eljc/article/view/v11i1n9 %X It is shown that if a $d$-regular graph contains $s$ vertices so that the distance between any pair is at least $4k$, then its adjacency matrix has at least $s$ eigenvalues which are at least $2 d-1 \big(\pi2 k\big)$. A similar result has been proved by Friedman using more sophisticated tools.

@article{nilli12, abstract = { It is shown that if a $d$-regular graph contains $s$ vertices so that the distance between any pair is at least $4k$, then its adjacency matrix has at least $s$ eigenvalues which are at least $2 \sqrt {d-1} \cos \big({\pi\over 2 k}\big)$. A similar result has been proved by Friedman using more sophisticated tools. }, added-at = {2017-02-24T12:52:38.000+0100}, author = {Nilli, A.}, biburl = {https://www.bibsonomy.org/bibtex/238a8f58e0b51e90cd506f42a9fd52c75/ytyoun}, description = {Tight Estimates for Eigenvalues of Regular Graphs | Nilli | The Electronic Journal of Combinatorics}, interhash = {c10a26d3370a97cc64b4b4e53d00377c}, intrahash = {38a8f58e0b51e90cd506f42a9fd52c75}, keywords = {alon-boppana eigenvalues expander graph.theory ramanujan serre}, timestamp = {2017-02-24T12:52:38.000+0100}, title = {Tight Estimates for Eigenvalues of Regular Graphs}, url = {http://www.combinatorics.org/ojs/index.php/eljc/article/view/v11i1n9}, year = 2012 }