TY - JOUR
ID - 13980
TI - On the super domination number of graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Rodriguez-Velazquez, Juan Alberto
AU - Klein, Douglas F.
AU - Yi, Eunjeong
AD - Universitat Rovira i Virgili
AD - Texas A&M University
AD - Texas A&M University
Y1 - 2020
PY - 2020
VL - 5
IS - 2
SP - 83
EP - 96
KW - Super domination number
KW - Domination number
KW - Cartesian product
KW - Corona product
DO - 10.22049/cco.2019.26587.1122
N2 - 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.
UR - http://comb-opt.azaruniv.ac.ir/article_13980.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13980_027a87bda526f67f2d8f3430aa9c2c45.pdf
ER -