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A dominator coloring of a graph G is a proper coloring in which every vertex of G dominates at least one color class. The dominator chromatic number of G,χd(G),is defined by the minimum number of colors needed in a dominator coloring of G. A total dominator coloring of G is a proper coloring of G with the extra property that every vertex in G properly dominates a color class. The total dominator chromatic number of G,χtd(G), is the minimum number of colors needed in a total dominator coloring of G. In this paper, we obtain dominator and total dominator chromatic number of Mongolian tent graphs and fire cracker graphs.

Dominator and total dominator chromatic number of Mongolian tent and fire cracker graphs