@article { author = {Alikhani, Saeid and Soltani, Samaneh}, title = {Distinguishing number (index) and domination number of a graph}, journal = {Khayyam Journal of Mathematics}, volume = {6}, number = {2}, pages = {199-205}, year = {2020}, publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)}, issn = {2423-4788}, eissn = {2423-4788}, doi = {10.22034/kjm.2020.109817}, abstract = {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.}, keywords = {distinguishing number,Distinguishing index,Domination number}, url = {https://www.kjm-math.org/article_109817.html}, eprint = {https://www.kjm-math.org/article_109817_a3bf156522e2b7558c7dc5148bbbdf86.pdf} }