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Total double Roman domination in graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 13، دوره 5، شماره 1، شهریور 2020، صفحه 27-39 اصل مقاله (428.53 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2019.26484.1118 | ||
| نویسندگان | ||
| Guoliang Hao* 1؛ Lutz Volkmann2؛ Doost Ali Mojdeh3 | ||
| 1College of Science, East China University of Technology, Nanchang, P. R. China | ||
| 2RWTH Aachen University | ||
| 3University of Mazandaran | ||
| چکیده | ||
| Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:V\rightarrow\{0,1,2,3\}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one vertex assigned $3$ under $f$, whereas if $f(v)=1$, then the vertex $v$ must be adjacent to at least one vertex assigned $2$ or $3$. The weight of a DRDF $f$ is the sum $\sum_{v\in V}f(v)$. A total double Roman dominating function (TDRDF) on a graph $G$ with no isolated vertex is a DRDF $f$ on $G$ with the additional property that the subgraph of $G$ induced by the set $\{v\in V:f(v)\ne0\}$ has no isolated vertices. The total double Roman domination number $\gamma_{tdR}(G)$ is the minimum weight of a TDRDF on $G$. In this paper, we give several relations between the total double Roman domination number of a graph and other domination parameters and we determine the total double Roman domination number of some classes of graphs. | ||
| کلیدواژه‌ها | ||
| total double Roman domination؛ double Roman domination؛ total Roman domination؛ total domination؛ domination | ||
| مراجع | ||
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