Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

On the kth Laplacian eigenvalues of trees with perfect matchings

Language

English

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). © 2009 Elsevier Inc. All rights reserved.

Keywords

Bound, Laplacian eigenvalue, Perfect matchings, Tree

Publication Date

2010

Source Publication Title

Linear Algebra and its Applications

Volume

432

Issue

4

Start Page

1036

End Page

1041

Publisher

Elsevier

DOI

10.1016/j.laa.2009.10.015

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.laa.2009.10.015

ISSN (print)

00243795

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