Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)Khayyam Journal of Mathematics2423-47886220200701Distinguishing number (index) and domination number of a graph19920510981710.22034/kjm.2020.109817ENSaeidAlikhaniDepartment of Mathematics, Yazd University, 89195-741, Yazd, Iran0000-0002-1801-203XSamanehSoltaniDepartment of Mathematics, Yazd University, 89195-741, Yazd, IranJournal Article20190127The distinguishing number (index) of a graph $G$ is the least integer $d$<br /> 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.https://www.kjm-math.org/article_109817_a3bf156522e2b7558c7dc5148bbbdf86.pdf