Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

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

Graph, Eigenvalue, Adding an edge, Energy

Publication Date

7-2018

Source Publication Title

Linear Algebra and its Applications

Volume

548

Start Page

57

End Page

65

Publisher

Elsevier

Peer Reviewed

1

Copyright

© 2018 Elsevier Inc. All rights reserved.

Funder

Partially supported by NSF of China(No.11371372); Program for New Century Ex- cellent Talents in Fujian Province University; Project of Fujian Education Department (No.JZ160455); Research Fund of Minnan Normal University (No.MX1603).

DOI

10.1016/j.laa.2018.02.012

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.laa.2018.02.012

ISSN (print)

00243795

Available for download on Saturday, August 01, 2020

Included in

Mathematics Commons

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