Rank numbers of grid graphs

A ranking of a graph is a labeling of the vertices with positive integers such that any path between vertices of the same label contains a vertex of greater label. The rank number of a graph is the smallest possible number of labels in a ranking. We find rank numbers of the Möbius ladder, K_s×P_n, and P₃×P_n. We also find bounds for rank numbers of general grid graphs P_m×P_n.