A new upper bound on the largest normalized Laplacian eigenvalue (Q2852253)
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scientific article; zbMATH DE number 6213941
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new upper bound on the largest normalized Laplacian eigenvalue |
scientific article; zbMATH DE number 6213941 |
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A new upper bound on the largest normalized Laplacian eigenvalue (English)
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8 October 2013
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normalized Laplacian matrix
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Randić matrix
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upper bound
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largest eigenvalue
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subdominant eigenvalue
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The authors prove that the largest normalized Laplacian eigenvalue \(\lambda_1\) of a simple connected graph \(G\) is bounded from above by NEWLINE\[NEWLINE 2-\min_{i\sim j} \left\{ \frac{|N_i\cap N_j|}{\max\{d_i,d_j\}} \right\}, NEWLINE\]NEWLINE where the minimum is taken over all pairs of adjacent vertices \(i\), \(j\) (here \(N_i\) is the set of vertices adjacent to \(i\) and \(d_i=|N_i|\) is the degree of \(i\)).
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