Isoperimetric bounds for the first eigenvalue of the Laplacian
โ Scribed by Qiaoling Wang; Changyu Xia
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 120 KB
- Volume
- 61
- Category
- Article
- ISSN
- 0044-2275
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๐ SIMILAR VOLUMES
We give a lower bound for the second smallest eigenvalue of Laplacian matrices in terms of the isoperimetric number of weighted graphs. This is used to obtain an upper bound for the real parts of the nonmaximal eigenvalues of irreducible nonnegative matrices.
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