Some results on graphs with exactly two main eigenvalues

Yaoping Hou; Zikai Tang; Wai Chee Shiu

doi:10.1016/j.aml.2011.11.025

Some results on graphs with exactly two main eigenvalues

Yaoping Hou^*, Zikai Tang, Wai Chee Shiu

^*Corresponding author for this work

Department of Mathematics

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

15 Citations (Scopus)

Abstract

An eigenvalue of a graph G is called main if there is an associated eigenvector not orthogonal to j, the vector with each entry equal to 1. In this work, an error in a prior paper [Y. Hou and F. Tian, Unicyclic graphs with exactly two main eigenvalues, Appl. Math. Letters, 19 (2006), 1143-1147] is pointed out and the properties of the graphs with exactly two main eigenvalues and with pendent vertices are discussed. As an application, we obtain, together with known results, all connected bicyclic and tricyclic graphs with exactly two main eigenvalues.

Original language	English
Pages (from-to)	1274-1278
Number of pages	5
Journal	Applied Mathematics Letters
Volume	25
Issue number	10
DOIs	https://doi.org/10.1016/j.aml.2011.11.025
Publication status	Published - Oct 2012

User-Defined Keywords

2-walk linear graphs
Bicyclic graphs
Main eigenvalues
Tricyclic graphs

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10.1016/j.aml.2011.11.025

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title = "Some results on graphs with exactly two main eigenvalues",

abstract = "An eigenvalue of a graph G is called main if there is an associated eigenvector not orthogonal to j, the vector with each entry equal to 1. In this work, an error in a prior paper [Y. Hou and F. Tian, Unicyclic graphs with exactly two main eigenvalues, Appl. Math. Letters, 19 (2006), 1143-1147] is pointed out and the properties of the graphs with exactly two main eigenvalues and with pendent vertices are discussed. As an application, we obtain, together with known results, all connected bicyclic and tricyclic graphs with exactly two main eigenvalues.",

keywords = "2-walk linear graphs, Bicyclic graphs, Main eigenvalues, Tricyclic graphs",

author = "Yaoping Hou and Zikai Tang and Shiu, {Wai Chee}",

note = "Funding Information: The first author was supported by the National Natural Science Fund of China (No. 10771061 , 11171102 ). The last author was supported by: GRF, Research Grant Council of Hong Kong ; FRG, Hong Kong Baptist University . The authors would like to express their sincere gratitude to the referees for careful reading and valuable suggestions, which led to a number of improvements in this work.",

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AU - Hou, Yaoping

AU - Tang, Zikai

AU - Shiu, Wai Chee

N1 - Funding Information: The first author was supported by the National Natural Science Fund of China (No. 10771061 , 11171102 ). The last author was supported by: GRF, Research Grant Council of Hong Kong ; FRG, Hong Kong Baptist University . The authors would like to express their sincere gratitude to the referees for careful reading and valuable suggestions, which led to a number of improvements in this work.

PY - 2012/10

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N2 - An eigenvalue of a graph G is called main if there is an associated eigenvector not orthogonal to j, the vector with each entry equal to 1. In this work, an error in a prior paper [Y. Hou and F. Tian, Unicyclic graphs with exactly two main eigenvalues, Appl. Math. Letters, 19 (2006), 1143-1147] is pointed out and the properties of the graphs with exactly two main eigenvalues and with pendent vertices are discussed. As an application, we obtain, together with known results, all connected bicyclic and tricyclic graphs with exactly two main eigenvalues.

AB - An eigenvalue of a graph G is called main if there is an associated eigenvector not orthogonal to j, the vector with each entry equal to 1. In this work, an error in a prior paper [Y. Hou and F. Tian, Unicyclic graphs with exactly two main eigenvalues, Appl. Math. Letters, 19 (2006), 1143-1147] is pointed out and the properties of the graphs with exactly two main eigenvalues and with pendent vertices are discussed. As an application, we obtain, together with known results, all connected bicyclic and tricyclic graphs with exactly two main eigenvalues.

KW - 2-walk linear graphs

KW - Bicyclic graphs

KW - Main eigenvalues

KW - Tricyclic graphs

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U2 - 10.1016/j.aml.2011.11.025

DO - 10.1016/j.aml.2011.11.025

M3 - Journal article

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VL - 25

SP - 1274

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JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

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ER -

Some results on graphs with exactly two main eigenvalues

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