Edge connectivity is a crucial measure of the robustness of a network. Several edge connectivity variants have been proposed for measuring the reliability and fault tolerance of networks under various conditions. Let G be a connected graph, S be a subset of edges in G, and k be a positive integer. If $G-S$ is disconnected and every component has at least k vertices, then S is a k-extra edge-cut of G. The k-extra edge-connectivity, denoted by ${\lambda }_k(G)$, is the minimum cardinality over all k-extra edge-cuts of G. If ${\lambda }_k(G)$ exists and at least one component of $G-S$ contains exactly k vertices for any minimum k-extra edge-cut S, then G is super-${\lambda }_k$. Moreover, when G is super-${\lambda }_k$, the persistence of G, denoted by ${\rho }_k(G)$, is the maximum integer m for which $G-F$ is still super-${\lambda }_k$ for any set $F\subseteq E(G)$ with $|F|\le m$. Previously, bounds of ${\rho }_k(G)$ were provided only for $k\in \{1,2\}$. This study provides the bounds of ${\rho }_k(G)$ for $k\ge 2$.

边缘连接性是衡量网络健壮性的关键指标。已经提出了几种边缘连通性变型，用于测量各种条件下网络的可靠性和容错性。令G为连通图，S为G中边的子集，k为正整数。如果$G-\mathrm{小号}$被断开，每一个部件具有至少ķ顶点，然后小号是K-额外边缘切割的ģ。第k个额外的边缘连接性，表示为${\lambda }_{ķ}（G）$是G的所有k个额外边沿上的最小基数。如果${\lambda }_{ķ}（G）$ 存在并且至少一个组成部分 $G-\mathrm{小号}$对于任何最小的k-额外的边切割S，它精确地包含k个顶点，则G是超-${\lambda }_{ķ}$。而且，当G超级时${\lambda }_{ķ}$，G的持久性，表示为${\rho }_{ķ}（G）$，是最大整数米为其$G-F$ 还是超级${\lambda }_{ķ}$ 对于任何一组 $F\subseteq Ë（G）$ 与 $|F|\le 米$。以前，${\rho }_{ķ}（G）$ 仅提供给 $ķ\in \{\mathrm{1个}，2\}$。这项研究提供了${\rho }_{ķ}（G）$ 对于 $ķ\ge 2$。