Dominator colorings of Cartesian product of graphs

A dominator coloring of a graph G is a proper coloring of G in which each vertex dominates all the vertices of at least one color class. The dominator chromatic number chi(d)(G) of G is the minimum number of colors required for a dominator coloring of G. In [Dominator Colorings of Certain Cartesian Products of Paths and Cycles, Graphs and Combinatorics, Vol. 33 No. 1 (2017) 73-83], the dominator chromatic numbers of Cartesian product graphs P2OP,., and P-2 square C-n were determined. In this paper, we continue this study on Cartesian product graphs P-3 square P-n, P-3 square C-n, for n >= 3 and K-m square K-n, for m, n >= 2.