Super restricted edge connected Cartesian product graphs

Abstract

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 ′ .