Fractional Roman Domination
نویسندگان
چکیده
A function f : V (G) → {0, 1, 2} is a Roman dominating function if for every vertex with f(v) = 0, there exists a vertex w ∈ N(v) with f(w) = 2. We introduce two fractional Roman domination parameters, γR ◦ f and γRf , from relaxations of two equivalent integer programming formulations of Roman domination (the former using open neighborhoods and the later using closed neighborhoods in the Roman domination integer program). We show γf (G) ≤ γR ◦ f (G) ≤ 2γf (G), for all graphs G. We define a graph to be fractionally Roman if γR ◦ f (G) = 2γf (G). We find some classes of fractionally Roman graphs, and some classes which are not fractionally Roman.
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