Lower bounds for the eigenvalues of Laplacian matrices

By Abraham Berman, Xiaodong Zhang. 2000

67 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/e8e59731c89673e3ab0e54dbb91fbd2eca521868

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. J. Alexander Fax
2. Lihua Xie
3. Mehran Mesbahi
4. Yoonsoo Kim
5. M. Fu
6. N. Abreu

In Discrete Mathematics and Combinatorics

1. J. Alexander Fax
2. Mehran Mesbahi
3. Yoonsoo Kim
4. N. Abreu

In Geometry and Topology

1. J. Alexander Fax
2. Lihua Xie
3. Mehran Mesbahi
4. Yoonsoo Kim
5. N. Abreu
6. Richard M. Murray

Citations in the corpus

• On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian (2006, methodology): “Also related to the present work are those by Chung and Oden [5] pertaining to bounding the gap between the first two eigenvalues of graph Laplacians, and Berman and Zhang [2] and Guattery and Miller [11], where, respectively, isoperimetric numbers of weighted graphs and graph embeddings are employe”
• Distributed Consensus With Limited Communication Data Rate (2011, background): “3 of [41], a key property of a -expander is”
• Old and new results on algebraic connectivity of graphs (2007, background): “Both of them are proved by Zhang [74].”
• Optimal and Cooperative Control of Vehicle Formations (2002, result): “led to the definition of Cheeger constants for graphs in an analogous fashion to their definition for Riemannian manifolds, which in turn bound the eigenvalues of L; again, see [24], and [3, 43, 81] for more recent results.”