Some results on the Laplacian eigenvalues of unicyclic graphs

Jianxi Li; Wai Chee Shiu; Wai Hong Chan

doi:10.1016/j.laa.2008.11.016

Some results on the Laplacian eigenvalues of unicyclic graphs

Jianxi Li, Wai Chee Shiu^*, Wai Hong Chan

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

16 Citations (Scopus)

Abstract

In this paper, we provide the smallest value of the second largest Laplacian eigenvalue for any unicyclic graph, and find the unicyclic graphs attaining that value. And also give an "asymptotically good" upper bounds for the second largest Laplacian eigenvalues of unicyclic graphs. Using this results, we can determine unicyclic graphs with maximum Laplacian separator. And unicyclic graphs with maximum Laplacian spread will also be determined.

Original language	English
Pages (from-to)	2080-2093
Number of pages	14
Journal	Linear Algebra and Its Applications
Volume	430
Issue number	8-9
DOIs	https://doi.org/10.1016/j.laa.2008.11.016
Publication status	Published - 15 Apr 2009

Scopus Subject Areas

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

User-Defined Keywords

Laplacian eigenvalues
Laplacian separator
Laplacian spread
Unicyclic graphs

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10.1016/j.laa.2008.11.016

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title = "Some results on the Laplacian eigenvalues of unicyclic graphs",

abstract = "In this paper, we provide the smallest value of the second largest Laplacian eigenvalue for any unicyclic graph, and find the unicyclic graphs attaining that value. And also give an {"}asymptotically good{"} upper bounds for the second largest Laplacian eigenvalues of unicyclic graphs. Using this results, we can determine unicyclic graphs with maximum Laplacian separator. And unicyclic graphs with maximum Laplacian spread will also be determined.",

keywords = "Laplacian eigenvalues, Laplacian separator, Laplacian spread, Unicyclic graphs",

author = "Jianxi Li and Shiu, {Wai Chee} and Chan, {Wai Hong}",

note = "Funding Information: Partially supported by GRF, Research Grant Council of Hong Kong; FRG, Hong Kong Baptist University. ∗ Corresponding author. E-mail addresses: [email protected] (W.C. Shiu), [email protected] (W.H. Chan).",

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doi = "10.1016/j.laa.2008.11.016",

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T1 - Some results on the Laplacian eigenvalues of unicyclic graphs

AU - Li, Jianxi

AU - Shiu, Wai Chee

AU - Chan, Wai Hong

N1 - Funding Information: Partially supported by GRF, Research Grant Council of Hong Kong; FRG, Hong Kong Baptist University. ∗ Corresponding author. E-mail addresses: [email protected] (W.C. Shiu), [email protected] (W.H. Chan).

PY - 2009/4/15

Y1 - 2009/4/15

N2 - In this paper, we provide the smallest value of the second largest Laplacian eigenvalue for any unicyclic graph, and find the unicyclic graphs attaining that value. And also give an "asymptotically good" upper bounds for the second largest Laplacian eigenvalues of unicyclic graphs. Using this results, we can determine unicyclic graphs with maximum Laplacian separator. And unicyclic graphs with maximum Laplacian spread will also be determined.

AB - In this paper, we provide the smallest value of the second largest Laplacian eigenvalue for any unicyclic graph, and find the unicyclic graphs attaining that value. And also give an "asymptotically good" upper bounds for the second largest Laplacian eigenvalues of unicyclic graphs. Using this results, we can determine unicyclic graphs with maximum Laplacian separator. And unicyclic graphs with maximum Laplacian spread will also be determined.

KW - Laplacian eigenvalues

KW - Laplacian separator

KW - Laplacian spread

KW - Unicyclic graphs

UR - http://www.scopus.com/inward/record.url?scp=61449155311&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2008.11.016

DO - 10.1016/j.laa.2008.11.016

M3 - Journal article

AN - SCOPUS:61449155311

SN - 0024-3795

VL - 430

SP - 2080

EP - 2093

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 8-9

ER -

Some results on the Laplacian eigenvalues of unicyclic graphs

Abstract

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