  The distinguishing index of a graph $G$, denoted by $D'(G)$, is the least
number of labels in an edge labeling of $G$ not preserved by any non-trivial
automorphism. The distinguishing chromatic index $\chi'_D (G)$ of a graph $G$
is the least number $d$ such that $G$ has a proper edge labeling with $d$
labels that is preserved only by the identity automorphism of $G$. In this
paper we compute the distinguishing chromatic index for some specific graphs.
Also we study the distinguishing chromatic index of corona product and join of
two graphs.
