  We introduce the total dominator edge chromatic number of a graph $G$. A
total dominator edge coloring (briefly TDE-coloring) of $G$ is a proper edge
coloring of $G$ in which each edge of the graph is adjacent to every edge of
some color class. The total dominator edge chromatic number (briefly
TDEC-number) $\chi'^t_d(G)$ of $G$ is the minimum number of color classes in a
TDE-coloring of $G$. We obtain some properties of $\chi'^t_d(G)$ and compute
this parameter for specific graphs. We examine the effects on $\chi'^t_d(G)$
when $G$ is modified by operations on vertex and edge of $G$. Finally, we
consider the $k$-subdivison of $G$ and study TDEC-number of this kind of
graphs.
