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The Laplacian spectral radius of graphs on surfaces

✍ Scribed by Liang Lin

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 89 KB
Volume: 428
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.08.032

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✦ Synopsis

Let G be an n-vertex (n 3) simple graph embeddable on a surface of Euler genus γ (the number of crosscaps plus twice the number of handles). Denote by the maximum degree of G. In this paper, we first present two upper bounds on the Laplacian spectral radius of G as follows:

(i)

(ii) If G is 4-connected and either the surface is the sphere or the embedding is 4-representative, then

Some upper bounds on the Laplacian spectral radius of the outerplanar and Halin graphs are also given.

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