On the second largest Laplacian eigenvalues of graphs

Jianxi Li; Ji Ming Guo; Wai Chee SHIU

doi:10.1016/j.laa.2012.10.047

On the second largest Laplacian eigenvalues of graphs

Jianxi Li^*, Ji Ming Guo, Wai Chee SHIU

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2438-2446
Number of pages	9
Journal	Linear Algebra and Its Applications
Volume	438
Issue number	5
DOIs	https://doi.org/10.1016/j.laa.2012.10.047
Publication status	Published - 1 Mar 2013

Scopus Subject Areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

User-Defined Keywords

Graph
Laplacian separator
Second largest Laplacian eigenvalue

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10.1016/j.laa.2012.10.047

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title = "On the second largest Laplacian eigenvalues of graphs",

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.",

keywords = "Graph, Laplacian separator, Second largest Laplacian eigenvalue",

author = "Jianxi Li and Guo, {Ji Ming} and SHIU, {Wai Chee}",

note = "Funding Information: Partially supported by the NSF of China (Nos. 11101358, 10871204); NSF of Fujian (Nos. 2011J05014, 2011J01026); Project of Fujian Education∗ Correspondingauthor.Department(Nos.JA11165, JA12208, JA12209); FRG, Hong Kong Baptist University. E-mail addresses: ptjxli@hotmail.com (J. Li), jimingguo@hotmail.com (J.-M. Guo), wcshiu@hkbu.edu.hk (W.C. Shiu).",

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doi = "10.1016/j.laa.2012.10.047",

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AU - Li, Jianxi

AU - Guo, Ji Ming

AU - SHIU, Wai Chee

N1 - Funding Information: Partially supported by the NSF of China (Nos. 11101358, 10871204); NSF of Fujian (Nos. 2011J05014, 2011J01026); Project of Fujian Education∗ Correspondingauthor.Department(Nos.JA11165, JA12208, JA12209); FRG, Hong Kong Baptist University. E-mail addresses: ptjxli@hotmail.com (J. Li), jimingguo@hotmail.com (J.-M. Guo), wcshiu@hkbu.edu.hk (W.C. Shiu).

PY - 2013/3/1

Y1 - 2013/3/1

N2 - 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.

AB - 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.

KW - Graph

KW - Laplacian separator

KW - Second largest Laplacian eigenvalue

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U2 - 10.1016/j.laa.2012.10.047

DO - 10.1016/j.laa.2012.10.047

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VL - 438

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EP - 2446

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 5

ER -

On the second largest Laplacian eigenvalues of graphs

Abstract

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