## 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.)

### Keywords:

Cartesian product; dominating set; domination number
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### References:

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