On super connectivity of Cartesian product graphs
The super connectivity kappa(1) 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 K. This article provides bounds for the super connectivity kappa(1) 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 kappa(1) (K-m x K-n) = min (m + 2n - 4,2m + n - 4] for m + n > 6 and state sufficient conditions to guarantee kappa(1) (K-2 x G) = 2 kappa (G). As a consequence, we immediately obtain the super connectivity of the n-cube for n > 3. (C) 2008 Wiley Periodicals, Inc.
super connectivity cartesian product maximally connected graphs super connected graphs