On super connectivity of Cartesian product graphs

The super connectivity κ1 of a connected graph G is the minimum number of vertices whose deletion results in a disconnected graph without isolated vertices; this is a more refined index than the connectivity parameter κ. This article provides bounds for the super connectivity κ1 of the Cartesian product of two connected graphs, and thus generalizes the main result of Shieh on the super connectedness of the Cartesian product of two regular graphs with maximum connectivity. Particularly, we determine that κ1(Km × Kn) = minlm + 2n - 4, 2m + n - 4r for m + n ≥ 6 and state sufficient conditions to guarantee κ1(K2 × G) = 2κ(G). As a consequence, we immediately obtain the super connectivity of the n-cube for n ≥ 3. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008

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