On the Laplacian spectral radii of trees with perfect matchings

摘要

Denote by T(2k){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 T(2k){mathcal{T}(2k)} and gave the corresponding tree T in T(2k){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 T(2k){mathcal{T}(2k)} and also give the corresponding trees T in T(2k){mathcal{T}(2k)} whose μ(T) reach these values.