The connectivity of a graph is an important issue in graph theory and is also one of the most important factors in evaluating the reliability and fault tolerance of a network. A graph G is called m-edge-fault-tolerant strongly Menger (m-EFTSM for short) edge connected if there are $\min \{{\mathrm{deg}}_{G-F}(x),{\mathrm{deg}}_{G-F}(y)\}$ edge-disjoint paths between any two different vertices x and y in $G-F$ for any $F\subseteq E(G)$ with $|F|\le m$.

In this paper, we give a necessary and sufficient condition of EFTSM edge connectivity on regular graphs. And we obtain several optimal results about EFTSM edge connectivity on (1, 2)-matching composition networks, each of which is constructed by connecting two graphs via one or two perfect matchings. As applications, we show that the class of n-dimensional hypercube-like networks (included hypercube, crossed cube et al.) are $(n-2)$-EFTSM edge connected; show that the n-dimensional folded hypercube is $(n-1)$-EFTSM edge connected, and show that the n-dimensional augmented cube is $(2n-3)$-EFTSM edge connected. The bounds $(n-2),(n-1)$ and $(2n-3)$ are sharp.

图的连通性是图论中的重要问题，也是评估网络的可靠性和容错性的最重要因素之一。如果存在，则将图G称为m边缘容错强Menger（简称为m -EFTSM）边缘连接$\mathrm{分}\{{\mathrm{度}}_{G-F}（X），{\mathrm{度}}_{G-F}（ÿ）\}$任何两个不同的顶点之间的边缘不相交的路径X和ÿ在$G-F$ 对于任何 $F\subseteq Ë（G）$ 与 $|F|\le 米$。

在本文中，我们在规则图上给出了EFTSM边缘连通性的充要条件。并且我们获得了关于（1，2）匹配合成网络上EFTSM边缘连通性的几个最佳结果，每个结果都是通过一个或两个完美匹配连接两个图而构造的。作为应用程序，我们证明了n维超立方体样网络（包括超立方体，交叉立方体等）的类是$（ñ-2）$-EFTSM边缘连接；证明n维折叠超立方体是$（ñ-\mathrm{1个}）$-EFTSM边连接，并显示n维增强立方体为$（2ñ-3）$-EFTSM边缘已连接。界限$（ñ-2），（ñ-\mathrm{1个}）$ 和 $（2ñ-3）$ 敏锐。