  Given a graph $G$, the total dominator coloring problem seeks a proper
coloring of $G$ with the additional property that every vertex in the graph is
adjacent to all vertices of a color class. We seek to minimize the number of
color classes. We study this problem on several classes of graphs, as well as
finding general bounds and characterizations. We also show the relation between
total dominator chromatic number and chromatic number and total domination
number.
