Edge-connectivity in regular multigraphs from eigenvalues

Suil O

Let $G$ be a $d$-regular multigraph, and let ${\lambda }_2(G)$ be the second largest eigenvalue of $G$. In this paper, we prove that if ${\lambda }_2(G)<\frac{d-1+\sqrt{9d^2-10d+17}}{4}$, then $G$ i…