An approximate version of Brouwer's Laplacian conjecture

Alan Lew

Let $G=(V,E)$ be an $n$-vertex graph, $L(G)\in {\mathbb{R}}^{n\times n}$ its Laplacian matrix, and let ${\lambda }_1(L(G))\ge {\lambda }_2(L(G))\ge \cdots \ge {\lambda }_n(L(G))=0$ denote its eigenvalues. For $…