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Roman Domination on Circular-Convex, Triad-Convex Bipartite Graphs and $P_4$-Tidy Graphs
The Roman Domination Problem (RDP) on a graph \(G=(V,E)\) asks for a labeling function \(f:V\rightarrow\{0,1,2\}\) such that every vertex assigned value \(0\) is adjacent to a vertex assigned value \(2\). The objective is to minimize the total weight \(\sum_{v\in V} f(v)\); this minimum value is the
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