Total dominator chromatic number of a graph

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Given a graph $G$, the total dominator coloring problem seeks aproper coloring of $G$ with the additional property that everyvertex in the graph is adjacent to all vertices of a color class. Weseek to minimize the number of color classes. We initiate to studythis problem on several classes of graphs, as well as findinggeneral bounds and characterizations. We also compare the totaldominator chromatic number of a graph with the chromatic number andthe total domination number of it.