## 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
โฆ LIBER โฆ
A note on the kth eigenvalue of trees
โ Scribed by Ji-Ming Guo
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 103 KB
- Volume
- 413
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The kth Laplacian eigenvalue of a tree
โ
Ji-Ming Guo
๐
Article
๐
2006
๐
John Wiley and Sons
๐
English
โ 102 KB
The Kth largest eigenvalue of a tree
โ
Hong Yuan
๐
Article
๐
1986
๐
Elsevier Science
๐
English
โ 214 KB
Sharp bound of the kth eigenvalue of tre
โ
Jiansheng Chen
๐
Article
๐
1994
๐
Elsevier Science
๐
English
โ 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.
The proof on the conjecture of extremal
โ
Jiansheng Chen
๐
Article
๐
2007
๐
Elsevier Science
๐
English
โ 311 KB
A note on the second largest eigenvalue
โ
Ji-Ming Guo; Shang-Wang Tan
๐
Article
๐
2004
๐
Elsevier Science
๐
English
โ 201 KB
On multiple eigenvalues of trees
โ
P. Rowlinson
๐
Article
๐
2010
๐
Elsevier Science
๐
English
โ 115 KB