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

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)57-65
Number of pages9
JournalLinear Algebra and Its Applications
Volume548
DOIs
Publication statusPublished - 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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