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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In this paper, we show that upper bounds of 2-rainbow dominationnumbers of several classes of graphs.
📌 3 Key Takeaways
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Objective & Hypothesis:A 2-rainbow domination function of a graph G is a function f that assigns to each vertex a set ofcolors chosen from the set {1,2}, such that for any 𝑣 ∈ 𝑉(𝐺), 𝑓(𝑣) = ∅ implies ⋃𝑢∈𝑁(𝑣) |𝑓(𝑣)| ={1,2}.
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Key Findings & Data:The 2-rainbow domination number 𝛾𝑟2(𝐺) of a graph G is minimum w(𝑓) = Σ𝑣∈𝑉(𝐺) |𝑓(𝑣)|over all such functions f.
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Conclusion & Impact:In this paper, we show that upper bounds of 2-rainbow dominationnumbers of several classes of graphs.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Vulnerability · domination · 2-rainbow domination
Abstract
A 2-rainbow domination function of a graph G is a function f that assigns to each vertex a set ofcolors chosen from the set {1,2}, such that for any 𝑣 ∈ 𝑉(𝐺), 𝑓(𝑣) = ∅ implies ⋃𝑢∈𝑁(𝑣) |𝑓(𝑣)| ={1,2}. The 2-rainbow domination number 𝛾𝑟2(𝐺) of a graph G is minimum w(𝑓) = Σ𝑣∈𝑉(𝐺) |𝑓(𝑣)|over all such functions f. In this paper, we show that upper bounds of 2-rainbow dominationnumbers of several classes of graphs.
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Cite This Article
DURGUN, D. D., ALTINDAĞ, F. N. (2016). 2-Rainbow Domination Number of Some Graphs. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, Cilt: 12 - Sayı: 3, 363–366. https://ajindex.com/articles/115382