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Roman Domination In Graphs

E. Cockayne, Paul A. Dreyer, S. M. Hedetniemi, S. Hedetniemi
Published 2004 · Mathematics, Computer Science

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Abstract A Roman dominating function on a graph G=(V,E) is a function f : V→{0,1,2} satisfying the condition that every vertex u for which f(u)=0 is adjacent to at least one vertex v for which f(v)=2. The weight of a Roman dominating function is the value f(V)=∑u∈Vf(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G. In this paper, we study the graph theoretic properties of this variant of the domination number of a graph.
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