On upper bounds for Laplacian graph eigenvalues
β Scribed by Dongmei Zhu
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 150 KB
- Volume
- 432
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
In this paper, we first obtain a sharp upper bound for the eigenvalues of the adjacency matrix of the line graph of a graph. Then this result is used to present a sharp upper bound for the Laplacian eigenvalues. Another sharp upper bound is presented also. Moreover, we determine all extreme graphs w
We consider weighted graphs, where the edge weights are positive definite matrices. The Laplacian of the graph is defined in the usual way. We obtain an upper bound on the largest eigenvalue of the Laplacian and characterize graphs for which the bound is attained. The classical bound of Anderson and