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

Mustapha Chellali; Nader Jafari Rad

Discussiones Mathematicae Graph Theory (2013)

- Volume: 33, Issue: 2, page 337-346
- ISSN: 2083-5892

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topMustapha Chellali, and Nader Jafari Rad. "Strong Equality Between the Roman Domination and Independent Roman Domination Numbers in Trees." Discussiones Mathematicae Graph Theory 33.2 (2013): 337-346. <http://eudml.org/doc/268140>.

@article{MustaphaChellali2013,

abstract = {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).},

author = {Mustapha Chellali, Nader Jafari Rad},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {Roman domination; independent Roman domination; strong equality; trees},

language = {eng},

number = {2},

pages = {337-346},

title = {Strong Equality Between the Roman Domination and Independent Roman Domination Numbers in Trees},

url = {http://eudml.org/doc/268140},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Mustapha Chellali

AU - Nader Jafari Rad

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

JO - Discussiones Mathematicae Graph Theory

PY - 2013

VL - 33

IS - 2

SP - 337

EP - 346

AB - 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).

LA - eng

KW - Roman domination; independent Roman domination; strong equality; trees

UR - http://eudml.org/doc/268140

ER -

## References

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