Abstract
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.
Keywords:
Acknowledgments
The authors are grateful to the referees for a short proof of in Theorem 3.3 and the outline of the proof of Theorem 3.6. They also thank the referees for their valuable comments, corrections, and suggestions which lead to a great improvement of this work.
This study was supported by National Natural Science Foundation of China (No. 10371075 and No. 10531070).