## Super edge- and point-connectivities of the Cartesian product of regular graphs.(English)Zbl 1018.05056

The author proves that the Cartesian product of two regular graphs with maximum edge-connectivity (i.e., $$\lambda(G)= d(G)$$) is super edge-connected except for the case $$K_2\times K_n$$, $$n\geq 2$$. Here super edge-connected means $$\lambda(G)= d(G)$$ and each minimum edge-disconnectivity set isolates a vertex. Using this result (and a similar one about maximum vertex-connectivity) certain classes of networks which are recursively defined by Cartesian products are shown to possess super edge-connectivity (respectively, super vertex-connectivity).
Reviewer: M.Hager (Leonberg)

### MSC:

 05C40 Connectivity
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### References:

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