## On the domination number of the product of two cycles.(English)Zbl 1212.05192

Summary: Let $$G=(V,E)$$ be a graph. A subset $$D\subseteq V$$ is called a dominating set for $$G$$ if for every $$v\in V-D$$, $$v$$ is adjacent to some vertex in $$D$$. The domination number $$\gamma (G)$$ is equal to $$\min \{| D| \:D\text{ is a dominating set of }G\}$$.
In this paper we calculate the domination numbers $$\gamma (C_m\times C_n)$$ of the product of two cycles $$C_m$$ and $$C_n$$ of lengths $$m$$ and $$n$$ for $$m=5$$ and $$n\equiv 3\!\pmod 5$$, also for $$m=6,7$$ and arbitrary $$n$$.

### MSC:

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

### Keywords:

domination; dominating sets; graph products; cycles