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Two sharp upper bounds for the Laplacian eigenvalues

✍ Scribed by Xiao-Dong Zhang

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
168 KB
Volume
376
Category
Article
ISSN
0024-3795

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✦ Synopsis

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 which attain these upper bounds. In last, two examples illustrate that our results are, in some sense, best.

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