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Bounding the gap between extremal Laplacian eigenvalues of graphs

✍ Scribed by Felix Goldberg

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
101 KB
Volume
416
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let G be a graph whose Laplacian eigenvalues are 0 = Ξ» 1 Ξ» 2 β€’ β€’ β€’ Ξ» n . We investigate the gap (expressed either as a difference or as a ratio) between the extremal non-trivial Laplacian eigenvalues of a connected graph (that is Ξ» n and Ξ» 2 ). This gap is closely related to the average density of cuts in a graph. We focus here on the problem of bounding the gap from below.

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