The chromatic distinguishing index of certain graphs

Abstract The distinguishing index of a graph G , denoted by D ′ ( G ) , is the least number of labels in an edge coloring of G not preserved by any non-trivial automorphism. The distinguishing chromatic index χ D ′ ( G ) of a graph G is the least number d such that G has a proper edge coloring 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.