For a graph $G$, let $λ_2(G)$ denote its second smallest Laplacian eigenvalue. It was conjectured that $λ_2(G) + λ_2(\overline G) \ge 1$, where $\overline G$ is the complement of $G$. In this paper, it is shown that $\max\{λ_2(G), λ_2(\overline G)\} \ge 2/5$.
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