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The proof on the conjecture of extremal graphs for the kth eigenvalues of trees

✍ Scribed by Jiansheng Chen

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
311 KB
Volume
426
Category
Article
ISSN
0024-3795

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πŸ“œ SIMILAR VOLUMES

The kth Laplacian eigenvalue of a tree
The kth Laplacian eigenvalue of a tree
✍ Ji-Ming Guo πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 102 KB

## Abstract Let Ξ»~__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

Sharp bound of the kth eigenvalue of tre
Sharp bound of the kth eigenvalue of trees
✍ Jiansheng Chen πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 585 KB

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.