Stratification and domination in prisms

A graph G is 2-stratified if its vertex set is partitioned into two classes (each of which is a stratum or a color class). We color the vertices in one color class red and the other color class blue. Let X be a 2-stratified graph with one fixed blue vertex υ specified. We say that X is rooted at υ. The X-domination number of a graph G is the minimum number of red vertices of G in a red-blue coloring of the vertices of G such that every blue vertex υ of G belongs to a copy of X rooted at υ. In this paper we investigate the X-domination number of prisms when X is a 2-stratified 4-cycle rooted at a blue vertex.