Dominator and Total Dominator Coloring on Square Chessboard

The proper coloring of a graph G is said to be a dominator coloring if each vertex of the graph dominates every vertex of some color class. The minimum number of color classes required to satisfy the condition of dominator coloring is said to be dominator chromatic number which is denoted by χd(G). Total dominator coloring is defined to be a proper coloring of G with a property that every vertex of G dominates all the vertices of at least one color class (other than the class itself). The minimum number of color classes required to satisfy the condition of total dominator coloring is called total dominator chromatic number and is denoted by χtd(G). In this paper, we would discuss the dominator and total dominator coloring parameters of bishops and rooks on square chessboard and give the values for dominator chromatic number and total dominator chromatic number for these chessboard graphs.