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On the Laplacian spectral radii of trees with nearly perfect matchings

Authors:	Li Zhang Jiayu Shao

Institution:	(1) Department of Applied Mathematics, Shanghai Finance University, Shanghai, 201209, China;(2) Department of Mathematics, Tongji University, Shanghai, 200092, China

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. This research is supported by the National Natural Science Foundation of China under Grant No. 10331020.

Keywords:	Tree Laplacian eigenvalue nearly perfect matching perfect matching
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