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 lambda'(G) of G. A graph G is said to be lambda'-optimal if lambda'(G) = xi(G), where xi(G) is the minimum edge-degree of G. A graph is said to be super-lambda' if every minimum restricted edge-cut isolates an edge. This article gives a sufficient condition for Cartesian product graphs to be super-lambda'. Using this result, certain classes of networks which are recursively defined by the Cartesian product can be simply shown to be super-lambda'. (C) 2009 Elsevier B.V. All rights reserved.
cartesian product lambda '-optimal super-lambda ' combinatorial problems