Six classes of trees with largest normalized algebraic connectivity

Jianxi Li*, Ji Ming Guo, Wai Chee SHIU, An Chang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

7 Citations (Scopus)


The normalized algebraic connectivity of a graph G, denoted by λ2(G), is the second smallest eigenvalue of its normalized Laplacian matrix. In this paper, we firstly determine all trees with λ2(G)≥1-63. Then we classify such trees into six classes C1,...,C6 and prove that λ2( Ti)>λ2(Tj) for 1≤i<j≤6, where TiCi and TjCj. At the same time, the values of the normalized algebraic connectivity for the six classes of trees are provided, respectively. These results are similar to those on the algebraic connectivity which were obtained by Yuan et al. (2008) [8].

Original languageEnglish
Pages (from-to)318-327
Number of pages10
JournalLinear Algebra and Its Applications
Publication statusPublished - 1 Jul 2014

Scopus Subject Areas

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

User-Defined Keywords

  • Normalized algebraic connectivity
  • Tree


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