Distinguishing number and distinguishing index of certain graphs
  The distinguishing number (index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling (edge labeling) with $d$ labels that is preserved only by a trivial automorphism. In this paper we compute these two parameters for some specific graphs. Also we study the distinguishing number and the distinguishing index of corona product of two graphs. 
Saeid Alikhani and Samaneh Soltani
math.CO