Displaying similar documents to “Introducing an Orientation into a Given Non-Directed Graph”

Strong Equality Between the Roman Domination and Independent Roman Domination Numbers in Trees

Mustapha Chellali, Nader Jafari Rad (2013)

Discussiones Mathematicae Graph Theory

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A Roman dominating function (RDF) 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 an RDF is the value f(V (G)) = P u2V (G) f(u). An RDF f in a graph G is independent if no two vertices assigned positive values are adjacent. The Roman domination number R(G) (respectively, the independent Roman domination number iR(G)) is the minimum weight of an...