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 language | English |
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Pages (from-to) | 1036-1041 |
Number of pages | 6 |
Journal | Linear Algebra and Its Applications |
Volume | 432 |
Issue number | 4 |
DOIs | |
Publication status | Published - 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