- Tytuł:
- Strong Equality Between the Roman Domination and Independent Roman Domination Numbers in Trees
- Autorzy:
-
Chellali, Mustapha
Rad, Nader Jafari - Powiązania:
- https://bibliotekanauki.pl/articles/30146596.pdf
- Data publikacji:
- 2013-05-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
Roman domination
independent Roman domination
strong equality
trees - 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) $.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2013, 33, 2; 337-346
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł