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Paper IPM / M / 11516  


Abstract:  
A Roman dominating function on a graph G is a labeling f : V(G) → {0,1,2} such that every vertex with label 0 has a neighbor with label 2.
A set {f_{1},f_{2},...,f_{d}} of Roman dominating functions on G with the property that Σ_{i=1}^{d}f_{i}(v) ≤ 2 for each v ∈ V(G) is called a
Roman dominating family (of functions) on G. The maximum number of functions in a Roman dominating family on G is the Roman domatic number of G, denoted by d_{R}(G). this work we initiate the study of the Roman domatic number in graphs and we present some sharp bounds for d_{R}(G). In addition, we determine the Roman domatic number of some graphs.
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