Document Type: Original Article
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran
The distinguishing number (index) of a graph $G$ is the least integer $d$
such that $G$ has a vertex labeling (edge labeling) with $d$ labels that is preserved only by the trivial automorphism. A set $S$ of vertices in $G$ is a dominating set of $G$ if every vertex of $V(G)\setminus S$ is adjacent to some vertex in $S$. The minimum cardinality of a dominating set of $G$ is the domination number of $G$. In this paper, we obtain some upper bounds for the distinguishing number and the distinguishing index of a graph based on its domination number.