On the extreme eigenvalues of regular graphs
| dc.creator | Cioaba, Sebastian M. | |
| dc.date | 2004-07-15 | |
| dc.date | 2005-08-12 | |
| dc.date.accessioned | 2026-07-07T05:10:22Z | |
| dc.date.available | 2026-07-07T05:10:22Z | |
| dc.description | In this paper, we present an elementary proof of a theorem of Serre concerning the greatest eigenvalues of $k$-regular graphs. We also prove an analogue of Serre's theorem regarding the least eigenvalues of $k$-regular graphs: given $ε>0$, there exist a positive constant $c=c(ε,k)$ and a nonnegative integer $g=g(ε,k)$ such that for any $k$-regular graph $X$ with no odd cycles of length less than $g$, the number of eigenvalues $μ$ of $X$ such that $μ\leq -(2-ε)\sqrt{k-1}$ is at least $c|X|$. This implies a result of Winnie Li. | |
| dc.description | accepted to J.Combin.Theory, Series B. added 5 new references, some comments on the constant c in Section 2 | |
| dc.identifier | https://arxiv.org/abs/math/0407274 | |
| dc.identifier | http://arxiv.org/abs/math/0407274 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71908 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C50;15A18 | |
| dc.title | On the extreme eigenvalues of regular graphs | |
| dc.type | text |