  We introduce and study the dominated edge coloring of a graph. A dominated
edge coloring of a graph $G$ is a proper edge coloring of $G$ such that each
color class is dominated by at least one edge of $G$. The minimum number of
colors among all dominated edge coloring is called the dominated edge chromatic
number, denoted by $\chi_{dom}^{\prime}(G)$. We obtain some properties of
$\chi_{dom}^{\prime}(G)$ and compute it for specific graphs. Also we examine
the effects on $\chi_{dom}^{\prime}(G)$ when $G$ is modified by operations on
vertex and edge of $G$. Finally, we consider the $k$-subdivision of $G$ and
study the dominated edge chromatic number of these kind of graphs.
