Stack Domination Density

There are infinite sequences of graphs {Gn} where |Gn| = n such that the minimal dominating sets for H × Gi fall into predictable patterns, in light of which γ(Gn × H) may be nearly linear in n; the coefficient of linearity may be regarded as the average density of the dominating set in the H-fibers of the product. The specific cases where the sequence {Gn} consists of cycles or path is explored in detail, and the domination density of the Grötzsch graph is calculated. For more general sequences {Gn}, the conditions under which this density exists are explored.