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Discussiones Mathematicae Graph Theory

2013 | 33 | 2 | 337-346

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

EN

Abstrakty

EN
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 RDF (respectively, independent RDF) on G. We say that R(G) strongly equals iR(G), denoted by R(G) ≡ iR(G), if every RDF on G of minimum weight is independent. In this paper we provide a constructive characterization of trees T with R(T) ≡ iR(T).

EN

337-346

wydano
2013-05-01
online
2013-04-13

Twórcy

autor
• LAMDA-RO, Department of Mathematics University of Blida B.P. 270, Blida, Algeria
autor
• Department of Mathematics, Shahrood University of Technology Shahrood, Iran and School of Mathematics Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

Bibliografia

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