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

Jing Huang, Chunyan Qin

Let $G=(V,E)$ be a finite simple graph with Laplacian eigenvalues $\hat{I}{»}_1(L(G))\ge \cdots \ge \hat{I}{»}_{|V|}(L(G))$, and define \[ \eps_k(G)= \sum_{j=1}^{\min\{k,|V|\}}λ_j(L(G))-|E|. \] Let…