Jing Huang

A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality

Let $G=(V,E)$ be a finite simple graph with Laplacian eigenvalues $\lambda_1(L(G))\ge\cdots\ge\lambda_{|V|}(L(G))$, and define \[ \eps_k(G)= \sum_{j=1}^{\min\{k,|V|\}}\lambda_j(L(G))-|E|. \] Let $\nu(G)$ be the matching number of $G$, and let $n(G)$ be the number of non-isolated vertices of $G$. Lew proved that \(\eps_...