## The domination number of $$C_8 \times C_n$$ and $$C_9 \times C_n$$.(English)Zbl 0935.05070

Summary: A set $$D$$ of vertices of a simple graph $$G= (V,E)$$ is called dominating if every vertex $$v\in V-D$$ is adjacent to some vertex $$\mu\in D$$. The domination number of a graph $$G$$, $$\Gamma(G)$$, is the order of a smallest dominating set of $$G$$. We calculate the domination numbers of the toroidal grid graphs $$C_8\times C_n$$ and $$C_9\times C_n$$. The domination numbers of $$C_m\times C_n$$, for $$m= 5$$ and $$n\equiv 3\pmod 5$$, and also for $$m= 6, 7$$ and arbitrary $$n$$ were calculated by the authors in a previous paper.

### MSC:

 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)

### Keywords:

domination number; dominating set; toroidal grid graphs