An edge-separating theorem on the second smallest normalized laplacian eigenvalue of a graph and its applications

Jianxi Li; Ji Ming Guo; Wai Chee SHIU; An Chang

doi:10.1016/j.dam.2014.02.020

An edge-separating theorem on the second smallest normalized laplacian eigenvalue of a graph and its applications

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

^*Corresponding author for this work

Department of Mathematics

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

13 Citations (Scopus)

Abstract

Let ^λ2(G) be the second smallest normalized Laplacian eigenvalue of a graph G. In this paper, we investigate the behavior on ^λ2(G) when the graph G is perturbed by separating an edge. This result can be used to determine all trees and unicyclic graphs with ^λ2(G)≥1-22. Moreover, the trees and unicyclic graphs with ^λ2(G)=1-22 are also determined, respectively.

Original language	English
Pages (from-to)	104-115
Number of pages	12
Journal	Discrete Applied Mathematics
Volume	171
DOIs	https://doi.org/10.1016/j.dam.2014.02.020
Publication status	Published - 10 Jul 2014

Scopus Subject Areas

Discrete Mathematics and Combinatorics
Applied Mathematics

User-Defined Keywords

Edge-separating
Second smallest normalized Laplacian eigenvalue
Tree
Unicyclic graph

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10.1016/j.dam.2014.02.020

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title = "An edge-separating theorem on the second smallest normalized laplacian eigenvalue of a graph and its applications",

abstract = "Let λ2(G) be the second smallest normalized Laplacian eigenvalue of a graph G. In this paper, we investigate the behavior on λ2(G) when the graph G is perturbed by separating an edge. This result can be used to determine all trees and unicyclic graphs with λ2(G)≥1-22. Moreover, the trees and unicyclic graphs with λ2(G)=1-22 are also determined, respectively.",

keywords = "Edge-separating, Second smallest normalized Laplacian eigenvalue, Tree, Unicyclic graph",

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

note = "Funding Information: Partially supported by NSF of China (Nos. 11101358 , 61379021 , 11371372 ); NSF of Fujian (Nos. 2011J05014 , 2011J01026 ); Project of Fujian Education Department (No. JA11165); Postdoctoral Foundation of Fuzhou University; General Research Fund of Hong Kong ; Faculty Research Grant of Hong Kong Baptist University . ",

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T1 - An edge-separating theorem on the second smallest normalized laplacian eigenvalue of a graph and its applications

AU - Li, Jianxi

AU - Guo, Ji Ming

AU - SHIU, Wai Chee

AU - Chang, An

N1 - Funding Information: Partially supported by NSF of China (Nos. 11101358 , 61379021 , 11371372 ); NSF of Fujian (Nos. 2011J05014 , 2011J01026 ); Project of Fujian Education Department (No. JA11165); Postdoctoral Foundation of Fuzhou University; General Research Fund of Hong Kong ; Faculty Research Grant of Hong Kong Baptist University .

PY - 2014/7/10

Y1 - 2014/7/10

N2 - Let λ2(G) be the second smallest normalized Laplacian eigenvalue of a graph G. In this paper, we investigate the behavior on λ2(G) when the graph G is perturbed by separating an edge. This result can be used to determine all trees and unicyclic graphs with λ2(G)≥1-22. Moreover, the trees and unicyclic graphs with λ2(G)=1-22 are also determined, respectively.

AB - Let λ2(G) be the second smallest normalized Laplacian eigenvalue of a graph G. In this paper, we investigate the behavior on λ2(G) when the graph G is perturbed by separating an edge. This result can be used to determine all trees and unicyclic graphs with λ2(G)≥1-22. Moreover, the trees and unicyclic graphs with λ2(G)=1-22 are also determined, respectively.

KW - Edge-separating

KW - Second smallest normalized Laplacian eigenvalue

KW - Tree

KW - Unicyclic graph

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U2 - 10.1016/j.dam.2014.02.020

DO - 10.1016/j.dam.2014.02.020

M3 - Article

AN - SCOPUS:84898542447

SN - 0166-218X

VL - 171

SP - 104

EP - 115

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

An edge-separating theorem on the second smallest normalized laplacian eigenvalue of a graph and its applications

Abstract

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