The effect on eigenvalues of connected graphs by adding edges

Ji Ming Guo; Pan Pan Tong; Jianxi Li; Wai Chee SHIU; Zhi Wen Wang

doi:10.1016/j.laa.2018.02.012

The effect on eigenvalues of connected graphs by adding edges

Ji Ming Guo^*, Pan Pan Tong, Jianxi Li, Wai Chee SHIU, Zhi Wen Wang

^*Corresponding author for this work

Department of Mathematics

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

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Abstract

By the well-known Perron–Frobenius Theorem [3], for a connected graph G, its largest eigenvalue strictly increases when an edge is added. We are interested in how the other eigenvalues of a connected graph change when edges are added. Examples show that all cases are possible: increased, decreased, unchanged. In this paper, we consider the effect on the eigenvalues by suitably adding edges in particular families, say the family of connected graphs with clusters. By using the result, we also consider the effect on the energy by suitably adding edges to the graphs of the above families.

Original language	English
Pages (from-to)	57-65
Number of pages	9
Journal	Linear Algebra and Its Applications
Volume	548
DOIs	https://doi.org/10.1016/j.laa.2018.02.012
Publication status	Published - 1 Jul 2018

Scopus Subject Areas

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

User-Defined Keywords

Adding an edge
Eigenvalue
Energy
Graph

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10.1016/j.laa.2018.02.012

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title = "The effect on eigenvalues of connected graphs by adding edges",

abstract = "By the well-known Perron–Frobenius Theorem [3], for a connected graph G, its largest eigenvalue strictly increases when an edge is added. We are interested in how the other eigenvalues of a connected graph change when edges are added. Examples show that all cases are possible: increased, decreased, unchanged. In this paper, we consider the effect on the eigenvalues by suitably adding edges in particular families, say the family of connected graphs with clusters. By using the result, we also consider the effect on the energy by suitably adding edges to the graphs of the above families.",

keywords = "Adding an edge, Eigenvalue, Energy, Graph",

author = "Guo, {Ji Ming} and Tong, {Pan Pan} and Jianxi Li and SHIU, {Wai Chee} and Wang, {Zhi Wen}",

note = "Funding Information: Partially supported by NSFC (No. 11371372); Program for New Century Excellent Talents in Fujian Province University; Project of Fujian Education Department (No. JZ160455); Research Fund of Minnan Normal University (No. MX1603).",

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AU - Guo, Ji Ming

AU - Tong, Pan Pan

AU - Li, Jianxi

AU - SHIU, Wai Chee

AU - Wang, Zhi Wen

N1 - Funding Information: Partially supported by NSFC (No. 11371372); Program for New Century Excellent Talents in Fujian Province University; Project of Fujian Education Department (No. JZ160455); Research Fund of Minnan Normal University (No. MX1603).

PY - 2018/7/1

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N2 - By the well-known Perron–Frobenius Theorem [3], for a connected graph G, its largest eigenvalue strictly increases when an edge is added. We are interested in how the other eigenvalues of a connected graph change when edges are added. Examples show that all cases are possible: increased, decreased, unchanged. In this paper, we consider the effect on the eigenvalues by suitably adding edges in particular families, say the family of connected graphs with clusters. By using the result, we also consider the effect on the energy by suitably adding edges to the graphs of the above families.

AB - By the well-known Perron–Frobenius Theorem [3], for a connected graph G, its largest eigenvalue strictly increases when an edge is added. We are interested in how the other eigenvalues of a connected graph change when edges are added. Examples show that all cases are possible: increased, decreased, unchanged. In this paper, we consider the effect on the eigenvalues by suitably adding edges in particular families, say the family of connected graphs with clusters. By using the result, we also consider the effect on the energy by suitably adding edges to the graphs of the above families.

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DO - 10.1016/j.laa.2018.02.012

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SP - 57

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JO - Linear Algebra and Its Applications

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ER -

The effect on eigenvalues of connected graphs by adding edges

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