Toughness and normalized Laplacian eigenvalues of graphs

Xueyi Huang, Kinkar Chandra Das, Shunlai Zhu

Given a connected graph $G$, the toughness ${\tau }_G$ is defined as the minimum value of the ratio $|S|/{\omega }_{G-S}$, where $S$ ranges over all vertex cut sets of $G$, and ${\omega }_{G-S}$ is the…