Geodesic
On dominating the Cartesian product of a graph and K₂
Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 3, pp. 389-402

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In this paper we consider the Cartesian product of an arbitrary graph and a complete graph of order two. Although an upper and lower bound for the domination number of this product follow easily from known results, we are interested in the graphs that actually attain these bounds. In each case, we provide an infinite class of graphs to show that the bound is sharp. The graphs that achieve the lower bound are of particular interest given the special nature of their dominating sets and are investigated further.
Keywords: domination, 2-packing, Cartesian product 
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     title = {On dominating the {Cartesian} product of a graph and {K₂}},
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Hartnell, Bert; Rall, Douglas. On dominating the Cartesian product of a graph and K₂. Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 3, pp. 389-402. http://geodesic.mathdoc.fr/item/DMGT_2004_24_3_a2/