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arXiv · 2607.03711

A linear algebraic proof of the Laplacian spread conjecture

Bocheng Li·Qingzhong Ji
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Abstract

For a graph $G,$ let $α(G)$ denote its second smallest Laplacian eigenvalue. The Laplacian Spread Conjecture is that $α(G)+α(\overline{G}) \geq 1,$ where $\overline{G}$ is the complement of $G.$ In this article, we provide a new proof of the Laplacian spread conjecture by means of linear algebra, which is more concise.

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Bocheng Li, Qingzhong Ji. 2026-07-04. A linear algebraic proof of the Laplacian spread conjecture. https://arxiv.org/abs/2607.03711

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