  Let $G$ be a simple graph. A total dominator coloring of $G$ is a proper
coloring of the vertices of $G$ in which each vertex of the graph is adjacent
to every vertex of some color class. The total dominator chromatic number
$\chi_d^t(G)$ of $G$ is the minimum number of colors among all total dominator
coloring of $G$. In this paper, we study the total dominator chromatic number
of some specific graphs.
