  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 (TDC) number
$\chi_d^t(G)$ of $G$, is the minimum number of colors among all total dominator
coloring of $G$. For any $k \in \mathbb{N}$, the $k$-subdivision of $G$ is a
simple graph $G^{\frac{1}{k}}$ which is constructed by replacing each edge of
$G$ with a path of length $k$. In this paper, we study the total dominator
chromatic number of $k$-subdivision of $G$.
