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The domination number of \(K_n^3\). (English) Zbl 1305.05175

Summary: Let \(K_n^3\) denote the Cartesian product \(K_n\square K_n\square K_n\), where \(K_n\) is the complete graph on \(n\) vertices. We show that the domination number of \(K_n^3\) is \(\lceil\frac{n^2}{2}\rceil\).

MSC:

05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C76 Graph operations (line graphs, products, etc.)
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