The chromatic distinguishing index of certain graphs

Abstract

The distinguishing index of a graph $G$, denoted by $D^{\prime }(G)$, is the least number of labels in an edge labeling of $G$ not preserved by any non-trivial automorphism. The distinguishing chromatic index ${\chi }_D^{\prime }(G)$ 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.

12 pages, 2 figures