Department of Mathematics, Yazd University, 89195-741, Yazd, Iran
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.
Alikhani, S., & Soltani, S. (2020). Distinguishing number (index) and domination number of a graph. Khayyam Journal of Mathematics, 6(2), 199-205. doi: 10.22034/kjm.2020.109817
MLA
Saeid Alikhani; Samaneh Soltani. "Distinguishing number (index) and domination number of a graph". Khayyam Journal of Mathematics, 6, 2, 2020, 199-205. doi: 10.22034/kjm.2020.109817
HARVARD
Alikhani, S., Soltani, S. (2020). 'Distinguishing number (index) and domination number of a graph', Khayyam Journal of Mathematics, 6(2), pp. 199-205. doi: 10.22034/kjm.2020.109817
VANCOUVER
Alikhani, S., Soltani, S. Distinguishing number (index) and domination number of a graph. Khayyam Journal of Mathematics, 2020; 6(2): 199-205. doi: 10.22034/kjm.2020.109817
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