On super edge-connectivity of Cartesian product graphs

The super edge-connectivity λ′ of a connected graph G is the minimum cardinality of an edge-cut F in G such that every component of G − F contains at least two vertices. LetGi be a connected graph with order ni , minimum degree δi and edge-connectivity λi for i = 1, 2. This article shows that λ′(G1 × G2) ≥ min{n1 λ2,n2 λ1,λ1 + 2λ2, 2λ1+λ2} forn1,n2 ≥ 3 andλ′(K2×G2) = min{n2, 2λ2}, which generalizes the main result of Shieh on the super edge-connectedness of the Cartesian product of two regular graphs with maximum edge-connectivity. In particular, this article determines λ′(G1 × G2) = min{n1 δ2, n2 δ1, ξ(G1 ×G2)} if λ′(Gi ) = ξ(Gi ), where ξ(G) is the minimum edge-degree of a graph G. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 49(2), 152–157 2007