On the kth Laplacian eigenvalues of trees with perfect matchings

Jianxi Li*, Wai Chee SHIU, An Chang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Let Tn+ be the set of all trees of order n with perfect matchings. In this paper, we prove that for any tree T ∈ Tn+, its kth largest Laplacian eigenvalue μk (T) satisfies μk (T) = 2 when n = 2 k, and μk (T) ≤ frac(⌈ frac(n, 2 k) ⌉ + 2 + sqrt((⌈ frac(n, 2 k) ⌉)2 + 4), 2) when n ≠ 2 k. Moreover, this upper bound is sharp when n = 0 (mod 2 k).

Original languageEnglish
Pages (from-to)1036-1041
Number of pages6
JournalLinear Algebra and Its Applications
Volume432
Issue number4
DOIs
Publication statusPublished - 1 Feb 2010

Scopus Subject Areas

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

User-Defined Keywords

  • Bound
  • Laplacian eigenvalue
  • Perfect matchings
  • Tree

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