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arXiv · 1806.06770

The Algebraic Connectivity of a Graph and its Complement

B. Afshari·S. Akbari·M. J. Moghaddamzadeh·B. Mohar
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Abstract

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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B. Afshari, S. Akbari, M. J. Moghaddamzadeh, B. Mohar. 2018-06-18. The Algebraic Connectivity of a Graph and its Complement. https://doi.org/10.1016/j.laa.2018.06.015

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