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The domination numbers of cylindrical grid graphs. (English) Zbl 1223.05214
Summary: Let $$\gamma (P_m \square C_n)$$ denote the domination number of the cylindrical grid graph formed by the Cartesian product of the graphs $$P_m$$, the path of length $$m,\, m \geqslant 2$$ and the graph $$C_n$$, the cycle of length $$n,\, n \geqslant 3$$. In this paper, methods to find the domination numbers of graphs of the form $$P_m \square C_n$$ with $$n geqslant 3$$ and $$m = 2, 3$$ and 4 are proposed. Moreover, bounds on domination numbers of the graphs $$P_{5} \square C_n, n \geqslant 3$$ are found. The methods that are used to prove that results readily lead to algorithms for finding minimum dominating sets of the above mentioned graphs.

##### MSC:
 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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