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
β¦ LIBER β¦
A nontrivial upper bound on the largest Laplacian eigenvalue of weighted graphs
β Scribed by Oscar Rojo
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 138 KB
- Volume
- 420
- Category
- Article
- ISSN
- 0024-3795
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We first give a result on eigenvalues of the line graph of a graph. We then use the result to present a new upper bound for eigenvalues of the Laplacian matrix of a graph. Moreover we determine all graphs the largest eigenvalue of whose Laplacian matrix reaches the upper bound.