Multiplicity of Laplacian eigenvalue 1 of a graph

Yuhao Zhou, Fenglei Tian

Let $G$ be a graph with $p(G)$ pendant vertices and $q(G)$ quasi-pendant vertices. Denote by $m_{L(G)}(\hat{I}»)$ the multiplicity of $\hat{I}»$ as a Laplacian eigenvalue of $G$. A graph $G$ i…