A bound on the Laplacian spread which is tight for strongly regular graphs

Fan Hsuan Lin; Chih-wen Weng

doi:10.1016/j.laa.2015.12.014

A bound on the Laplacian spread which is tight for strongly regular graphs

Fan Hsuan Lin^*, Chih-wen Weng

^*Corresponding author for this work

Department of Applied Mathematics

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

4 Scopus citations

Abstract

The Laplacian spread of a graph is the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of the graph. For Laplacian matrices of graphs, we find their upper bounds of largest eigenvalues, lower bounds of second-smallest eigenvalues and upper bounds of Laplacian spreads. The strongly regular graphs attain all the above bounds. Some other extremal graphs are also provided.

Original language	English
Pages (from-to)	11-22
Number of pages	12
Journal	Linear Algebra and Its Applications
Volume	494
DOIs	https://doi.org/10.1016/j.laa.2015.12.014
State	Published - 1 Apr 2016

Keywords

Laplacian matrix
Laplacian spread
Strongly regular graph

Access to Document

10.1016/j.laa.2015.12.014

Cite this

@article{47c75a91d4a84461bcca65e727acfe80,

title = "A bound on the Laplacian spread which is tight for strongly regular graphs",

abstract = "The Laplacian spread of a graph is the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of the graph. For Laplacian matrices of graphs, we find their upper bounds of largest eigenvalues, lower bounds of second-smallest eigenvalues and upper bounds of Laplacian spreads. The strongly regular graphs attain all the above bounds. Some other extremal graphs are also provided.",

keywords = "Laplacian matrix, Laplacian spread, Strongly regular graph",

author = "Lin, {Fan Hsuan} and Chih-wen Weng",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2016",

month = apr,

day = "1",

doi = "10.1016/j.laa.2015.12.014",

language = "English",

volume = "494",

pages = "11--22",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - A bound on the Laplacian spread which is tight for strongly regular graphs

AU - Lin, Fan Hsuan

AU - Weng, Chih-wen

PY - 2016/4/1

Y1 - 2016/4/1

N2 - The Laplacian spread of a graph is the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of the graph. For Laplacian matrices of graphs, we find their upper bounds of largest eigenvalues, lower bounds of second-smallest eigenvalues and upper bounds of Laplacian spreads. The strongly regular graphs attain all the above bounds. Some other extremal graphs are also provided.

AB - The Laplacian spread of a graph is the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of the graph. For Laplacian matrices of graphs, we find their upper bounds of largest eigenvalues, lower bounds of second-smallest eigenvalues and upper bounds of Laplacian spreads. The strongly regular graphs attain all the above bounds. Some other extremal graphs are also provided.

KW - Laplacian matrix

KW - Laplacian spread

KW - Strongly regular graph

UR - http://www.scopus.com/inward/record.url?scp=84954167861&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2015.12.014

DO - 10.1016/j.laa.2015.12.014

M3 - Article

AN - SCOPUS:84954167861

SN - 0024-3795

VL - 494

SP - 11

EP - 22

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

A bound on the Laplacian spread which is tight for strongly regular graphs

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this