Minimizing the Laplacian spectral radius of trees with given matching number

Let denote the set of trees on n vertices with fixed matching number β. In this article, we prove that if n = kβ +1, k ≥ 2, then the trees which minimize the Laplacian spectral radius over have maximum degree Δ =k, and determine the extremal trees for 1≤ β ≤4.

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