The distinguishing number and the distinguishing index of Cayley graphs

The distinguishing number (index) $D(G)$ ($D^{\mathrm{\prime }}(G)$) 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 investigate the distinguishing number and the distinguishing index of Cayley graphs.