A sharp upper bound on the largest eigenvalue of the Laplacian matrix of a graph

By Jinlong Shu, Yuan Hong, Kai Wen-Ren. 2002

75 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2eaf237329c3dd43b570d19a7b7e0b3385896ced

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Slobodan K. Simic
2. Dragos M. Cvetkovic
3. Xiaodong Zhang
4. Vladimir Nikiforov
5. Peter Rowlinson
6. Dragan Stevanovic
7. Mei Lu
8. Huiqing Liu

In Discrete Mathematics and Combinatorics

1. Peter Rowlinson
2. Dragos M. Cvetkovic
3. Slobodan K. Simic
4. Xiaodong Zhang

In Geometry and Topology

1. Slobodan K. Simic
2. Dragos M. Cvetkovic
3. Xiaodong Zhang
4. Vladimir Nikiforov
5. Peter Rowlinson
6. Dragan Stevanovic
7. Zoran Stanic
8. Pierre Hansen

Citations in the corpus

• Two sharp upper bounds for the Laplacian eigenvalues (2004, background): “[11] gave an upper bound in terms of degree sequences.”
• On the Laplacian spectral radius of a graph (2004, background): “In [ 11 ], Shu et al. prove a sharp upper bound as follows:”
• EIGENVALUE BOUNDS FOR THE SIGNLESS LAPLACIAN (2007, background): “The following theorem was proved implicitly in [22].”
• Bounding the largest eigenvalue of trees in terms of the largest vertex degree (2003, background): “Now, from (10) and (11) we have that λ1(B ∗) < ∆− 2 + 2 √ ∆− 1, and from (7) we finally obtain μ1(B∆,k) < ∆ + 2 √ ∆− 1.”