Super restricted edge connected Cartesian product graphs

An edge-cut F of a connected graph G is called a restricted edge-cut if G−F contains no isolated vertices. The minimum cardinality of all restricted edge-cuts is called the restricted edge-connectivity λ′(G) of G. A graph G is said to be λ′-optimal if λ′(G)=ξ(G), where ξ(G) is the minimum edge-degree of G. A graph is said to be super-λ′ if every minimum restricted edge-cut isolates an edge. This article gives a sufficient condition for Cartesian product graphs to be super-λ′. Using this result, certain classes of networks which are recursively defined by the Cartesian product can be simply shown to be super-λ′.