Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 5 2 2020 12 01 On the super domination number of graphs 83 96 13980 10.22049/cco.2019.26587.1122 EN Juan Alberto Rodríguez-Velázquez Universitat Rovira i Virgili Douglas F. Klein Texas A&M University Eunjeong Yi Texas A&M University Journal Article 2019 06 20 The open neighborhood of a vertex $v$ of a graph $G$ is the set $N(v)$ consisting of all vertices adjacent to $v$ in $G$. For $D\subseteq V(G)$, we define $\overline{D}=V(G)\setminus D$. A set $D\subseteq V(G)$ is called a super dominating set of $G$ if for every vertex $u\in \overline{D}$, there exists $v\in D$ such that  $N(v)\cap \overline{D}=\{u\}$. The super domination number of $G$ is the minimum cardinality among all super dominating sets of $G$. In this paper, we obtain closed formulas and tight bounds for the super domination number of $G$ in terms of several invariants of $G$. We also obtain results on the super domination number of corona product graphs and Cartesian product graphs. https://comb-opt.azaruniv.ac.ir/article_13980_027a87bda526f67f2d8f3430aa9c2c45.pdf