A decreasing sequence of upper bounds on the largest Laplacian eigenvalue of a graph
✍ Scribed by Oscar Rojo; Héctor Rojo
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 251 KB
- Volume
- 381
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
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
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.