The full chracterazation of the graphs with a L-eigenvalue of multiplicity $n-3$

Daijun Yin, Qiongxiang Huang

Let $\mathcal{G}(n,k)$ be the set of connected graphs of order $n$ with one of the Laplacian eigenvalue having multiplicity $k$. It is well known that $\mathcal{G}(n,n-1)=\{K_n\}$.…