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On the Laplacian spectral radii of trees with perfect matchings
Authors:Xi-Ying Yuan  Jia-Yu Shao  Chang-Xiang He
Institution:(1) Department of Mathematics, Shanghai University, Shanghai, 200444, China;(2) Department of Mathematics, Tongji University, Shanghai, 200092, China;(3) College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China
Abstract:Denote by $${\mathcal{T}(2k)}$$ the set of trees of order 2k with perfect matchings. GUO Guo, Linear Algebra Appl. 368:379–385, 2003.] determined the largest value of Laplacian spectral radii μ(T) of the trees T in $${\mathcal{T}(2k)}$$ and gave the corresponding tree T in $${\mathcal{T}(2k)}$$ whose μ(T) reaches this largest value. In this paper, we determine the second to the sixth largest values of μ(T) of the trees T in $${\mathcal{T}(2k)}$$ and also give the corresponding trees T in $${\mathcal{T}(2k)}$$ whose μ(T) reach these values.
Keywords:Tree  Perfect matching  Laplacian spectral radius
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