Characterizing Cartesian fixers and multipliers
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. Also in 2004, Burger,...