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Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

On the second largest Laplacian eigenvalues of graphs

Language

English

Abstract

The second largest Laplacian eigenvalue of a graph is the second largest eigenvalue of the associated Laplacian matrix. In this paper, we study extremal graphs for the extremal values of the second largest Laplacian eigenvalue and the Laplacian separator of a connected graph, respectively. All simple connected graphs with second largest Laplacian eigenvalue at most 3 are characterized. It is also shown that graphs with second largest Laplacian eigenvalue at most 3 are determined by their Laplacian spectrum. Moreover, the graphs with maximum and the second maximum Laplacian separators among all connected graphs are determined. © 2012 Elsevier Inc. All rights reserved.

Keywords

Graph, Laplacian separator, Second largest Laplacian eigenvalue

Publication Date

2013

Source Publication Title

Linear Algebra and Its Applications

Volume

438

Issue

5

Start Page

2438

End Page

2446

Publisher

Elsevier

ISSN (print)

00243795

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