Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21285220201201On the super domination number of graphs83961398010.22049/cco.2019.26587.1122ENJuan AlbertoRodriguez-VelazquezUniversitat Rovira i Virgili0000-0002-9082-7647Douglas F.KleinTexas A&M UniversityEunjeongYiTexas A&M UniversityJournal Article20190620The 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 $Dsubseteq V(G)$, we define $overline{D}=V(G)setminus D$. A set $Dsubseteq V(G)$ is called a super dominating set of $G$ if for every vertex $uin overline{D}$, there exists $vin D$ 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.http://comb-opt.azaruniv.ac.ir/article_13980_027a87bda526f67f2d8f3430aa9c2c45.pdf