Trees with extremal Laplacian eigenvalue multiplicity

Vinayak Gupta, Gargi Lather, R. Balaji

Let $T$ be a tree. Suppose $\lambda$ is an eigenvalue of the Laplacian matrix of $T$ with multiplicity $m_T(\lambda )$. It is known that $m_T(\lambda )\le p(T)-1$, where $p(T)$ is the number of…