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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally, the relation between weak $3$-domination and $3$-rainbow domination number of graphs will be investigated.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $G=(V,E)$ be a graph with the vertex set $V=V(G)$ and the edge set $E=E(G)$.
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Key Findings & Data:Let $k$ be a positive integer and $gamma_{rk}(G)$ ($gamma_{i_{rk}}(G)$) be $k$-rainbow domination (independent $k$-rainbow domination) number of a graph $G$.
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Conclusion & Impact:Finally, the relation between weak $3$-domination and $3$-rainbow domination number of graphs will be investigated.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
Let $G=(V,E)$ be a graph with the vertex set $V=V(G)$ and the edge set $E=E(G)$. Let $k$ be a positive integer and $gamma_{rk}(G)$ ($gamma_{i_{rk}}(G)$) be $k$-rainbow domination (independent $k$-rainbow domination) number of a graph $G$. In this paper, we study the $k$-rainbow domination and independent $k$-rainbow domination numbers of graphs. We obtain bounds for $gamma_{rk}(G-e)$ ($gamma_{i_{rk}}(G-e)$) in terms of $gamma_{rk}(G)$ ($gamma_{i_{rk}}(G)$). Finally, the relation between weak $3$-domination and $3$-rainbow domination number of graphs will be investigated.
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Cite This Article
MOJDEH, D. A., MANSOUR, Z. (2022). (Independent) $k$-Rainbow Domination of a Graph. Turkish Journal of Mathematics and Computer Science, Cilt: 12 - Sayı: 2, 128–135. https://ajindex.com/articles/609103