%0 Journal Article
%T On the super domination number of graphs
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Rodriguez-Velazquez, Juan Alberto
%A Klein, Douglas F.
%A Yi, Eunjeong
%D 2020
%\ 12/01/2020
%V 5
%N 2
%P 83-96
%! On the super domination number of graphs
%K Super domination number
%K Domination number
%K Cartesian product
%K Corona product
%R 10.22049/cco.2019.26587.1122
%X 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 $Dsubseteq V(G)$, 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.
%U http://comb-opt.azaruniv.ac.ir/article_13980_027a87bda526f67f2d8f3430aa9c2c45.pdf