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On the super domination number of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 1، دوره 5، شماره 2، اسفند 2020، صفحه 83-96 اصل مقاله (497.71 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2019.26587.1122 | ||
| نویسندگان | ||
| Juan Alberto Rodríguez-Velázquez* 1؛ Douglas F. Klein2؛ Eunjeong Yi3 | ||
| 1Universitat Rovira i Virgili | ||
| 2Texas A&M University | ||
| 3Texas A&M University | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Super domination number؛ Domination number؛ Cartesian product؛ Corona product | ||
| مراجع | ||
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