Denote by μk(L(T)) the k-th Laplacian eigenvalue of a tree T. Let Tk(2t) be the set of all trees of order 2tk with perfect matchings. In this note, the trees T in Tk(2t) with μk(L(T))=t+2+t2+42 are characterized, which solves Problem of J.X. Li, W.C. Shiu and A. Chang in  completely.
Linear Algebra and its Applications – Elsevier
Published: Aug 15, 2016
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