Algorithmic Results on Independent Roman {2}-Domination

Liu, Qiyun; Song, Yonghao; Shao, Zehui; Jiang, Huiqin

doi:10.22049/cco.2024.29156.1872

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	Algorithmic Results on Independent Roman {2}-Domination
Communications in Combinatorics and Optimization
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 10 شهریور 1403 اصل مقاله (1.46 M)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2024.29156.1872
نویسندگان
Qiyun Liu¹؛ Yonghao Song¹؛ Zehui Shao¹؛ Huiqin Jiang^* ²^{، 3}
¹Institute of Computing Science and Technology,Guangzhou University, Guangzhou 510006, China
²Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
³School of Computer Science of Information Technology, Qiannan Normal University for Nationalities, Duyun 558000, China
چکیده
An independent Roman $\{2\}$-dominating function (IR2DF) $f:V \rightarrow \{0, 1, 2\}$ in a graph $G=(V,E)$ has the properties that $\sum_{u\in N(v)}f(u) \geq 2$ if $f(v)=0$, and $f(u)=0$ for $u \in N(v)$ if $f(v) \geq 1$, where $v \in V$. The weight of an IR2DF in a graph $G$ is defined as the sum of its function values for all vertices, given by $\omega(f)=\sum_{v\in V}f(v)$. The independent Roman $\{2\}$-domination number of $G$, denoted $i_{\{R2\}}(G)$, is the minimum weight of all IR2DFs in $G$. In this paper, we prove that the independent Roman $\{2\}$-domination problem (IR2D) is NP-complete, even when restricted to chordal bipartite graphs. We then give an exact formula for the IR2D in corona graphs. Finally, we present two linear-time algorithms for solving IR2D for proper interval graphs and block-cactus graphs, respectively.
کلیدواژه‌ها
Independent Roman {2}-domination؛ Linear-time algorithm؛ NP-completeness؛ Proper interval graph؛ Block-cactus graph

مراجع
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Algorithmic Results on Independent Roman {2}-Domination