文献类型：期刊文献

英文题名：The effect on eigenvalues of connected graphs by adding edges

作者：Guo, Ji-Ming[1];Tong, Pan-Pan[1];Li, Jianxi[2];Shiu, Wai Chee[3];Wang, Zhi-Wen[1]

机构：[1]East China Univ Sci & Technol, Dept Math, Shanghai, Peoples R China;[2]Minnan Normal Univ, Dept Math & Informat Sci, Zhangzhou, Fujian, Peoples R China;[3]Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China

年份：2018

卷号：548

起止页码：57

外文期刊名：LINEAR ALGEBRA AND ITS APPLICATIONS

收录：;EI(收录号：20181004880633);WOS:【SCI-EXPANDED(收录号:WOS:000430902300004)】；

基金：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).

语种：英文

外文关键词：Graph; Eigenvalue; Adding an edge; Energy

摘要：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. (C) 2018 Elsevier Inc. All rights reserved.