中文摘要：

如果G-F不连通且每个连通分支至少含有两个顶点,则连通图G的边子集F称为限制边割.如果图G的每个最小限制边割都孤立G中的一条边,则称G是超限制边连通的（简称超λ′）.对于满足｜F｜≤m的任意子集FE（G）,超λ′图G的边容错性ρ′（G）是使得G-F仍是超λ′的最大整数m.这里给出了min{k1＋k2-1,υ1k2-2k1-2k2＋1,υ2k1-2k1-2k2＋1}≤ρ′（G1×G2）≤k1＋k2-1,其中,对每个i∈{1,2},Gi是阶为υi的ki正则ki边连通图且ki≥4,G1×G2是G1和G2的笛卡尔乘积.并给出了使得ρ′（G1×G2）=k1＋k2-1的一些充分条件.

英文摘要：

A subset F of edges in a connected graph G is a restricted edge-cut if G-F is disconnected and every component has at least two vertices.A graph Gis super restricted edgeconnected（super-λ′for short）if every minimum restricted edge-cut of Gisolates at least one edge.The edge fault-toleranceρ′（G）of a super-λ′graph Gis the maximum integer mfor which G-Fis still super-λ′for any subset F E（G）with｜F｜≤m.It was shown that min{k1＋k2-1,υ1k2-2k1-2k2 ＋1,υ2k1-2k1-2k2 ＋1}≤ρ′（G1×G2）≤k1 ＋k2-1,where Giis a ki-regular ki-edge-connected graph of orderυi with ki≥4for each i∈ {1,2}and G1×G2is the Cartesian product graph of G1 and G2.And some sufficient conditions such thatρ′（G1×G2）=k1＋k2-1were presented.