✦ LIBER ✦

Bounds on the kth eigenvalues of trees and forests

✍ Scribed by Jia-yu Shao

Book ID: 107826445
Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 617 KB
Volume: 149
Category: Article
ISSN: 0024-3795
DOI: 10.1016/0024-3795(91)90322-n

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Sharp bound of the kth eigenvalue of tre

Sharp bound of the kth eigenvalue of trees

✍ Jiansheng Chen 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 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.

A note on the kth eigenvalue of trees

✍ Ji-Ming Guo 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 103 KB

The kth Laplacian eigenvalue of a tree

✍ Ji-Ming Guo 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 102 KB

## Abstract Let λ~__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

The Kth largest eigenvalue of a tree

✍ Hong Yuan 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 214 KB

Sharp bounds on the eigenvalues of trees

✍ Shengbiao Hu 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 289 KB

Let λ 1 (T ) and λ 2 (T ) be the largest and the second largest eigenvalues of a tree T , respectively. We obtain the following sharp lower bound for λ 1 (T ): where d i is the degree of the vertex v i and m i is the average degree of the adjacent vertices of v i . Equality holds if and only if T i

Sharp lower bounds on the eigenvalues of

Sharp lower bounds on the eigenvalues of trees

✍ Hong Yuan 📂 Article 📅 1989 🏛 Elsevier Science 🌐 English ⚖ 295 KB