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Sums of Reciprocal Eigenvalues of the Laplacian

โœ Scribed by Bodo Dittmar


Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
230 KB
Volume
237
Category
Article
ISSN
0025-584X

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๐Ÿ“œ SIMILAR VOLUMES


The kth Laplacian eigenvalue of a tree
โœ Ji-Ming Guo ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 102 KB

## Abstract Let ฮป~__k__~(__G__) be the __k__th Laplacian eigenvalue of a graph __G__. It is shown that a tree __T__ with __n__ vertices has $\lambda\_{k}(T)\le \lceil { {n}\over{k}}\rceil$ and that equality holds if and only if __k__ < __n__, __k__|__n__ and __T__ is spanned by __k__ vertex disjoin

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Po lya and G. Szego showed in 1951 that for simply connected plane domains, the first eigenvalue of the Laplacian (with Dirichlet boundary conditions) is maximal for a disk, under a conformal mapping normalization. That is, if f (z) is a conformal map of a disk D onto a bounded, simply connected pla