Geodesic
Characterizing Cartesian fixers and multipliers
Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 1, pp. 161-175

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Let G ☐ H denote the Cartesian product of the graphs G and H. In 2004, Hartnell and Rall [On dominating the Cartesian product of a graph and K₂, Discuss. Math. Graph Theory 24(3) (2004), 389-402] characterized prism fixers, i.e., graphs G for which γ(G ☐ K₂) = γ(G), and noted that γ(G ☐ Kₙ) ≥ min|V(G)|, γ(G)+n-2. We call a graph G a consistent fixer if γ(G ☐ Kₙ) = γ(G)+n-2 for each n such that 2 ≤ n |V(G)|- γ(G)+2, and characterize this class of graphs.
Keywords: Cartesian product, prism fixer, Cartesian fixer, prism doubler, Cartesian multiplier, domination number 
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Benecke, Stephen; Mynhardt, Christina. Characterizing Cartesian fixers and multipliers. Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 1, pp. 161-175. http://geodesic.mathdoc.fr/item/DMGT_2012_32_1_a13/