Trees with extremal Laplacian eigenvalue multiplicity

Vinayak Gupta, Gargi Lather, R. Balaji

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