  A total dominator coloring of a graph $G$ is a proper coloring of $G$ in
which each vertex of the graph is adjacent to every vertex of some color class.
The total dominator chromatic number of a graph is the minimum number of color
classes in a total dominator coloring of it. Here, we study the total dominator
coloring on central graphs by giving some tight bounds for the total dominator
chromatic number of the central of a graph, join of two graphs and
Nordhaus-Gaddum-like relations. Also we will calculate the total dominator
chromatic number of the central of a path, a cycle, a wheel, a complete graph
and a complete multipartite graph.
