Say $A$ is Laplacian matrix of graph, which is a tree, and $\lambda _{i}$ the eigenvalues of $A$.Define $m_{T} (\lambda_{i}) $ to be the number of the $\lambda _{i} $(repeat of $\lambda _{i}$ ), and $p_{T}$ is the number of vertex with degree $1$.
How do I prove $$ m_{T} (\lambda_{i}) \le p_{T}-1?$$