The distance Roman domatic number of a graph
نویسندگان
چکیده
Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-distance Roman dominating function on G is a labeling f : V (G) → {0, 1, 2} such that every vertex with label 0 has a vertex with label 2 within distance k from each other. A set {f1, f2, . . . , fd} of k-distance Roman dominating functions on G with the property that ∑d i=1 fi(v) ≤ 2 for each v ∈ V (G), is called a k-distance Roman dominating family (of functions) on G. The maximum number of functions in a k-distance Roman dominating family on G is the kdistance Roman domatic number of G, denoted by dR(G). In this paper we initiate the study of k-distance Roman domatic number in graphs and we present some sharp bounds for dR(G). In addition, we determine the k-distance Roman domatic number of some graphs.
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