Upper Bounds for the Laplacian Graph Eigenvalues
β Scribed by Jiong Sheng Li; Yong Liang Pan
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2004
- Tongue
- English
- Weight
- 129 KB
- Volume
- 20
- Category
- Article
- ISSN
- 1439-7617
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π SIMILAR VOLUMES
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.
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