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The spectral radius of irregular graphs

โœ Scribed by Lingsheng Shi

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
135 KB
Volume
431
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

Let ฮป 1 be the largest eigenvalue and ฮป n the least eigenvalue of the adjacency matrix of a connected graph G of order n. We prove that if G is irregular with diameter D, maximum degree ฮ”, minimum degree ฮด and average degree d, then

.

The inequality improves previous bounds of various authors and implies two lower bounds on ฮป n which improve previous bounds of Nikiforov. It also gives some fine tuning of a result of Alon and Sudakov. A similar inequality is also obtained for the Laplacian spectral radius of a connected irregular graph.

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