Temat: strong equality - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: A note on the independent Roman domination in unicyclic graphs
Autorzy:: Chellali, M.
Rad, N. J.
Tematy:: Roman domination
independent Roman domination
strong equality; Pokaż więcej
Data publikacji:: 2012
Powiązania:: https://bibliotekanauki.pl/articles/255989.pdf Link otwiera się w nowym oknie
Źródło:: Opuscula Mathematica; 2012, 32, 4; 715-718
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Opis:: A Roman dominating function (RDF) on a graph G= (V, E) is a function ƒ : V → {0, 1, 2} satisfying the condition that every vertex u for which ƒ(u) = 0 is adjacent to at least one vertex v for which ƒ(v)=2. The weight of an RDF is the value [formula]. An RDF ƒ in a graph G is independent if no two vertices assigned positive values are adjacent. The Roman domination number ΥR (G) (respectively, the independent Roman domination number ΥR(G) is the minimum weight of an RDF (respectively, independent RDF) on G. We say that ΥR(G) strongly equals iR(G), denoted by ΥR(G) ≡ iR(G), if every RDF on G of minimum weight is independent. In this note we characterize all unicyclic graphs G with ΥR(G) ≡ iR(G).
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Strong Equality Between the Roman Domination and Independent Roman Domination Numbers in Trees
Autorzy:: Chellali, Mustapha
Rad, Nader Jafari
Tematy:: Roman domination
independent Roman domination
strong equality
trees; Pokaż więcej
Data publikacji:: 2013-05-01
Powiązania:: https://bibliotekanauki.pl/articles/30146596.pdf Link otwiera się w nowym oknie
Źródło:: Discussiones Mathematicae Graph Theory; 2013, 33, 2; 337-346
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Opis:: A Roman dominating function (RDF) on a graph $G = (V,E)$ is a function $ f : V \rightarrow {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)) = \Sigma_{u \in V (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 $ \gamma_R (G) $ (respectively, the independent Roman domination number $ i_R(G) $) is the minimum weight of an RDF (respectively, independent RDF) on $G$. We say that $ \gamma_R(G)$ strongly equals $ i_R(G)$, denoted by $ \gamma_R (G) \equiv i_R(G)$, if every RDF on $G$ of minimum weight is independent. In this paper we provide a constructive characterization of trees $T$ with $ \gamma_R(T) \equiv i_R(T) $.
Dostawca treści:: Biblioteka Nauki

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