The universal cyclic edge-connectivity of a graph G is the least k such that there exists a set of k edges whose removal disconnects G into components where every component contains a cycle. We show that for graphs of minimum degree at least 3 and girth g at least 4, the universal cyclic edge-connectivity is bounded above by \((\Delta -2)g\) where \(\Delta \) is the maximum degree. We then prove that if the second eigenvalue of the adjacency matrix of a d-regular graph of girth \(g\ge 4\) is sufficiently small, then the universal cyclic edge-connectivity is \((d-2)g\), providing a spectral condition for when this upper bound on universal cyclic edge-connectivity is tight.

图G的通用循环边连通性是最小k，使得存在一组k 个边，这些边的移除将G断开为每个组件包含一个循环的组件。我们表明，对于最小度数至少为 3 且周长g至少为 4 的图，通用循环边连接性以\((\Delta -2)g\)为界，其中\(\Delta \)是最大度数. 然后我们证明，如果周长\(g\ge 4\)的d -正则图的邻接矩阵的第二个特征值足够小，那么通用循环边连通性是\((d-2)g\)，当通用循环边连通性的这个上限很紧时，提供了一个频谱条件。