Tight Estimates for Eigenvalues of Regular Graphs

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Tight Estimates for Eigenvalues of Regular Graphs
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 cos( 2k ). A similar result has been proved by Friedman using more sophisticated tools. 1 The main result Let G = (V, E) be a simple d-regular graph on n vertices. let A be its adjacency matrix, and let 1(G) = d 2(G) . . . n(G) be its eigenvalues. Alon and Boppana ([1], see also [9], [11]) proved that for any fixed d and for any infinite family of of d-regular graphs Gi, lim inf 2(Gi) 2
Alon Nilli
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2004
Authors Alon Nilli
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