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Sharp bound of the kth eigenvalue of trees

โœ Scribed by Jiansheng Chen

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
585 KB
Volume
128
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

The sharp lower bound of the kth largest positive eigenvalue of a tree T with n vertices, and the sharp lower bound of the positive eigenvalues of such a tree Tare worked out in this study. A conjecture on the sharp bound of the kth eigenvalue of such a T is proved.

๐Ÿ“œ SIMILAR VOLUMES

The kth Laplacian eigenvalue of a tree
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

Bounds of eigenvalues of graphs
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โœ Yuan Hong ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 469 KB

The eigenvalues of a graph are the eigenvalues of its adjacency matrix. This paper presents an algebraically defined invariant system of a graph. We get some bounds of the eigenvalues of graphs and propose a few open problems.