A linear algebraic proof of the Laplacian spread conjecture

Bocheng Li, Qingzhong Ji

For a graph $G,$ let $\hat{I}\pm (G)$ denote its second smallest Laplacian eigenvalue. The Laplacian Spread Conjecture is that $\hat{I}\pm (G)+\hat{I}\pm (\overline{G})\ge 1,$ where $\overline{G}$ is the c…