On the Laplacian spectral radii of trees with nearly perfect matchings

Abstract

Let $\mathcal{T}_{2k + 1}$ be the set of trees on 2k+1 vertices with nearly perfect matchings, and let $\mathcal{S}_{2k + 2}$ be the set of trees on 2k + 2 vertices with perfect matchings. The largest Laplacian spectral radii of trees in $\mathcal{T}_{2k + 1}$ and $\mathcal{S}_{2k + 2}$ and the corresponding trees were given by Guo (2003). In this paper, the authors determine the second to the sixth largest Laplacian spectral radii among all trees in $\mathcal{T}_{2k + 1}$ and give the corresponding trees.