TY - JOUR ID - 109817 TI - Distinguishing number (index) and domination number of a graph JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Alikhani, Saeid AU - Soltani, Samaneh AD - Department of Mathematics, Yazd University, 89195-741, Yazd, Iran Y1 - 2020 PY - 2020 VL - 6 IS - 2 SP - 199 EP - 205 KW - distinguishing number KW - Distinguishing index KW - Domination number DO - 10.22034/kjm.2020.109817 N2 - 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. UR - https://www.kjm-math.org/article_109817.html L1 - https://www.kjm-math.org/article_109817_a3bf156522e2b7558c7dc5148bbbdf86.pdf ER -