ROMAN k-DOMINATION IN GRAPHS

@inproceedings{Kammerling2009ROMANKI,
  title={ROMAN k-DOMINATION IN GRAPHS},
  author={Karsten Kammerling and Lutz Volkmann},
  year={2009}
}
Let k be a positive integer, and let G be a simple graph with vertex set V (G). A Roman k-dominating function on G is a function f : V (G) ! {0,1,2} such that every vertex u for which f(u) = 0 is adjacent to at least k vertices v1,v2,...,vk with f(vi) = 2 for i = 1,2,...,k. The weight of a Roman k-dominating function is the value f(V (G)) = u2V (G) f(u). The minimum weight of a Roman k-dominating function on a graph G is called the Roman k-domination number ∞kR(G) of G. Note that the Roman 1… CONTINUE READING

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