Some results on graphs with exactly two main eigenvalues

Yaoping Hou*, Zikai Tang, Wai Chee SHIU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 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 languageEnglish
Pages (from-to)1274-1278
Number of pages5
JournalApplied Mathematics Letters
Volume25
Issue number10
DOIs
Publication statusPublished - Oct 2012

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • 2-walk linear graphs
  • Bicyclic graphs
  • Main eigenvalues
  • Tricyclic graphs

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