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Efficient algorithms for independent Roman domination on some classes of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 10، دوره 8، شماره 1، خرداد 2023، صفحه 127-140 اصل مقاله (513.2 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.27305.1228 | ||
| نویسنده | ||
| Abolfazl Poureidi* | ||
| Shahrood University of Technology | ||
| چکیده | ||
| Let $G=(V,E)$ be a given graph of order $n $. A function $f : V \to \{0,1, 2\}$ is an independent Roman dominating function (IRDF) on $G$ if for every vertex $v\in V$ with $f(v)=0$ there is a vertex $u$ adjacent to $v$ with $f(u)=2$ and $\{v\in V:f(v)> 0\}$ is an independent set. The weight of an IRDF $f$ on $G $ is the value $f(V)=\sum_{v\in V}f(v)$. The minimum weight of an IRDF among all IRDFs on $G$ is called the independent Roman domination number of~$G$. In this paper, we give algorithms for computing the independent Roman domination number of $G$ in $O(|V|)$ time when $G=(V,E)$ is a tree, unicyclic graph or proper interval graph. | ||
| کلیدواژهها | ||
| Independent Roman dominating function؛ Algorithm؛ Tree؛ Unicyclic graph؛ Proper interval graph | ||
| مراجع | ||
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