The trees with the second smallest normalized Laplacian eigenvalue at least 1−32

Xiaoguo Tian; Ligong Wang

doi:10.1016/j.dam.2016.12.010

The trees with the second smallest normalized Laplacian eigenvalue at least 1−32

Xiaoguo Tian, Ligong Wang

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

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

5 Scopus citations

Abstract

Let λ₂(G) be the second smallest normalized Laplacian eigenvalue of a graph G. In this paper, we determine all trees with λ₂(T)≥1−32. Meanwhile, if T is a tree of diameter 6, then we prove that λ₂(T)≤1−32. Moreover, we determine all trees of diameter d=3 or 6 with λ₂(T)=1−32.

Original language	English
Pages (from-to)	118-133
Number of pages	16
Journal	Discrete Applied Mathematics
Volume	220
DOIs	https://doi.org/10.1016/j.dam.2016.12.010
State	Published - 31 Mar 2017

Keywords

Second smallest normalized Laplacian eigenvalue
Tree

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10.1016/j.dam.2016.12.010

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title = "The trees with the second smallest normalized Laplacian eigenvalue at least 1−32",

abstract = "Let λ2(G) be the second smallest normalized Laplacian eigenvalue of a graph G. In this paper, we determine all trees with λ2(T)≥1−32. Meanwhile, if T is a tree of diameter 6, then we prove that λ2(T)≤1−32. Moreover, we determine all trees of diameter d=3 or 6 with λ2(T)=1−32.",

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author = "Xiaoguo Tian and Ligong Wang",

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year = "2017",

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doi = "10.1016/j.dam.2016.12.010",

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AU - Tian, Xiaoguo

AU - Wang, Ligong

PY - 2017/3/31

Y1 - 2017/3/31

N2 - Let λ2(G) be the second smallest normalized Laplacian eigenvalue of a graph G. In this paper, we determine all trees with λ2(T)≥1−32. Meanwhile, if T is a tree of diameter 6, then we prove that λ2(T)≤1−32. Moreover, we determine all trees of diameter d=3 or 6 with λ2(T)=1−32.

AB - Let λ2(G) be the second smallest normalized Laplacian eigenvalue of a graph G. In this paper, we determine all trees with λ2(T)≥1−32. Meanwhile, if T is a tree of diameter 6, then we prove that λ2(T)≤1−32. Moreover, we determine all trees of diameter d=3 or 6 with λ2(T)=1−32.

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KW - Tree

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DO - 10.1016/j.dam.2016.12.010

M3 - 文章

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SN - 0166-218X

VL - 220

SP - 118

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JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

The trees with the second smallest normalized Laplacian eigenvalue at least 1−32

Abstract

Keywords

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