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A new upper bound for eigenvalues of the laplacian matrix of a graph

✍ Scribed by Li Jiong-Sheng; Zhang Xiao-Dong

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
270 KB
Volume
265
Category
Article
ISSN
0024-3795

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✦ Synopsis

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.

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A sharp upper bound on the largest Laplacian eigenvalue of weighted graphs
✍ Kinkar Ch. Das; R.B. Bapat πŸ“‚ Article πŸ“… 2005 πŸ› Elsevier Science 🌐 English βš– 217 KB

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