Restricted edge-connectivity and minimum edge-degree

Let G be a connected graph and S C E(G). If G - S is disconnected without isolated vertices, then S is called a restricted edge-cut of G. The restricted edge-connectivity lambda' = lambda'(G) of G is the minimum cardinality over all restricted edge-cuits of G. A connected graph G is called V-connected, if lambda'(G) exists. For a lambda'-connected graph G, Esfahanian and Hakimi have shown, in 1988, that lambda'(G) less than or equal to xi(G), where (G) is the minimum edge-degree. A V-connected graph G is called lambda'-optimal, if lambda'(G) = (G). Let G(1) and G(2) be two disjoint lambda'-optimal graphs. In this paper we investigate the cartesian product G(1) x G(2) to be lambda'-optimal. In addition, we discuss the same question for another operation on G(1) and G(2), and we generalize a recent theorem of J.-M. Xu on non lambda'-optimal graphs.