| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4601827 | Linear Algebra and its Applications | 2010 | 8 Pages |
Abstract
Let k be a natural number and let G be a graph with at least k vertices. Brouwer conjectured that the sum of the k largest Laplacian eigenvalues of G is at most , where e(G) is the number of edges of G. We prove this conjecture for k=2. We also show that if G is a tree, then the sum of the k largest Laplacian eigenvalues of G is at most e(G)+2k-1.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
