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 -