Proof of a problem on Laplacian eigenvalues of trees

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• 作者：Xiying Yuan ^{xiyingyuan2007@hotmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A42 ; 05C50
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 August 2016
• 年：2016
• 卷：503
• 期：Complete
• 页码：180-189
• 全文大小：283 K

文摘

Denote by μ_k(L(T))${\mu }_k(L(T))$ the k-th Laplacian eigenvalue of a tree T  . Let T_k(2t)${\mathcal{T}}_k(2t)$ be the set of all trees of order 2tk$2tk$ with perfect matchings. In this note, the trees T   in T_k(2t)${\mathcal{T}}_k(2t)$ with ${\mu }_k(L\left(T\right))=\frac{t+2+\sqrt{t^2+4}}{2}$ are characterized, which solves Problem of J.X. Li, W.C. Shiu and A. Chang in [3] completely.