Six classes of trees with largest normalized algebraic connectivity

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

doi:10.1016/j.laa.2014.03.030

Six classes of trees with largest normalized algebraic connectivity

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

^*Corresponding author for this work

Department of Mathematics

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

7 Citations (Scopus)

Abstract

The normalized algebraic connectivity of a graph G, denoted by ^λ2(G), is the second smallest eigenvalue of its normalized Laplacian matrix. In this paper, we firstly determine all trees with ^λ2(G)≥1-63. Then we classify such trees into six classes ^C1,...,^C6 and prove that ^λ2( ^Ti)>^λ2(^Tj) for 1≤i<j≤6, where ^Ti∈^Ci and ^Tj∈^Cj. At the same time, the values of the normalized algebraic connectivity for the six classes of trees are provided, respectively. These results are similar to those on the algebraic connectivity which were obtained by Yuan et al. (2008) [8].

Original language	English
Pages (from-to)	318-327
Number of pages	10
Journal	Linear Algebra and Its Applications
Volume	452
DOIs	https://doi.org/10.1016/j.laa.2014.03.030
Publication status	Published - 1 Jul 2014

Scopus Subject Areas

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

User-Defined Keywords

Normalized algebraic connectivity
Tree

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10.1016/j.laa.2014.03.030

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title = "Six classes of trees with largest normalized algebraic connectivity",

abstract = "The normalized algebraic connectivity of a graph G, denoted by λ2(G), is the second smallest eigenvalue of its normalized Laplacian matrix. In this paper, we firstly determine all trees with λ2(G)≥1-63. Then we classify such trees into six classes C1,...,C6 and prove that λ2( Ti)>λ2(Tj) for 1≤iTi∈Ci and Tj∈Cj. At the same time, the values of the normalized algebraic connectivity for the six classes of trees are provided, respectively. These results are similar to those on the algebraic connectivity which were obtained by Yuan et al. (2008) [8].",

keywords = "Normalized algebraic connectivity, Tree",

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 , 2012D140 ); Project of Fujian Education Department (Nos. JA11165 , JA12208 , JA12209 ); Postdoctoral Foundation of Fuzhou University ; General Research Fund of Hong Kong (No. 601016 ); Faculty Research Grant of Hong Kong Baptist University (No. HKBU202413 ). ",

year = "2014",

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doi = "10.1016/j.laa.2014.03.030",

language = "English",

volume = "452",

pages = "318--327",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

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T1 - Six classes of trees with largest normalized algebraic connectivity

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 , 2012D140 ); Project of Fujian Education Department (Nos. JA11165 , JA12208 , JA12209 ); Postdoctoral Foundation of Fuzhou University ; General Research Fund of Hong Kong (No. 601016 ); Faculty Research Grant of Hong Kong Baptist University (No. HKBU202413 ).

PY - 2014/7/1

Y1 - 2014/7/1

N2 - The normalized algebraic connectivity of a graph G, denoted by λ2(G), is the second smallest eigenvalue of its normalized Laplacian matrix. In this paper, we firstly determine all trees with λ2(G)≥1-63. Then we classify such trees into six classes C1,...,C6 and prove that λ2( Ti)>λ2(Tj) for 1≤iTi∈Ci and Tj∈Cj. At the same time, the values of the normalized algebraic connectivity for the six classes of trees are provided, respectively. These results are similar to those on the algebraic connectivity which were obtained by Yuan et al. (2008) [8].

AB - The normalized algebraic connectivity of a graph G, denoted by λ2(G), is the second smallest eigenvalue of its normalized Laplacian matrix. In this paper, we firstly determine all trees with λ2(G)≥1-63. Then we classify such trees into six classes C1,...,C6 and prove that λ2( Ti)>λ2(Tj) for 1≤iTi∈Ci and Tj∈Cj. At the same time, the values of the normalized algebraic connectivity for the six classes of trees are provided, respectively. These results are similar to those on the algebraic connectivity which were obtained by Yuan et al. (2008) [8].

KW - Normalized algebraic connectivity

KW - Tree

UR - http://www.scopus.com/inward/record.url?scp=84899415495&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2014.03.030

DO - 10.1016/j.laa.2014.03.030

M3 - Journal article

AN - SCOPUS:84899415495

SN - 0024-3795

VL - 452

SP - 318

EP - 327

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Six classes of trees with largest normalized algebraic connectivity

Abstract

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