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Remarks on the restrained Italian domination number in graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 15، دوره 8، شماره 1، خرداد 2023، صفحه 183-191 اصل مقاله (359.78 K) | ||
| نوع مقاله: Short notes | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.27471.1269 | ||
| نویسنده | ||
| Lutz Volkmann* | ||
| RWTH Aachen University | ||
| چکیده | ||
| Let $G$ be a graph with vertex set $V(G)$. An Italian dominating function (IDF) is a function $f:V(G)\longrightarrow \{0,1,2\}$ having the property that that $f(N(u))\geq 2$ for every vertex $u\in V(G)$ with $f(u)=0$, where $N(u)$ is the neighborhood of $u$. If $f$ is an IDF on $G$, then let $V_0=\{v\in V(G): f(v)=0\}$. A restrained Italian dominating function (RIDF) is an Italian dominating function $f$ having the property that the subgraph induced by $V_0$ does not have an isolated vertex. The weight of an RIDF $f$ is the sum $\sum_{v\in V(G)}f(v)$, and the minimum weight of an RIDF on a graph $G$ is the restrained Italian domination number. We present sharp bounds for the restrained Italian domination number, and we determine the restrained Italian domination number for some families of graphs. | ||
| کلیدواژهها | ||
| Italian domination؛ restrained Italian domination؛ restrained domination | ||
| مراجع | ||
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