# On The Roman Domination Stable Graphs

Majid Hajian; Nader Jafari Rad

Discussiones Mathematicae Graph Theory (2017)

- Volume: 37, Issue: 4, page 859-871
- ISSN: 2083-5892

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topMajid Hajian, and Nader Jafari Rad. "On The Roman Domination Stable Graphs." Discussiones Mathematicae Graph Theory 37.4 (2017): 859-871. <http://eudml.org/doc/288471>.

@article{MajidHajian2017,

abstract = {A Roman dominating function (or just 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 f is the value f(V (G)) = Pu2V (G) f(u). The Roman domination number of a graph G, denoted by R(G), is the minimum weight of a Roman dominating function on G. A graph G is Roman domination stable if the Roman domination number of G remains unchanged under removal of any vertex. In this paper we present upper bounds for the Roman domination number in the class of Roman domination stable graphs, improving bounds posed in [V. Samodivkin, Roman domination in graphs: the class RUV R, Discrete Math. Algorithms Appl. 8 (2016) 1650049].},

author = {Majid Hajian, Nader Jafari Rad},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {Roman domination number; bound},

language = {eng},

number = {4},

pages = {859-871},

title = {On The Roman Domination Stable Graphs},

url = {http://eudml.org/doc/288471},

volume = {37},

year = {2017},

}

TY - JOUR

AU - Majid Hajian

AU - Nader Jafari Rad

TI - On The Roman Domination Stable Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2017

VL - 37

IS - 4

SP - 859

EP - 871

AB - A Roman dominating function (or just 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 f is the value f(V (G)) = Pu2V (G) f(u). The Roman domination number of a graph G, denoted by R(G), is the minimum weight of a Roman dominating function on G. A graph G is Roman domination stable if the Roman domination number of G remains unchanged under removal of any vertex. In this paper we present upper bounds for the Roman domination number in the class of Roman domination stable graphs, improving bounds posed in [V. Samodivkin, Roman domination in graphs: the class RUV R, Discrete Math. Algorithms Appl. 8 (2016) 1650049].

LA - eng

KW - Roman domination number; bound

UR - http://eudml.org/doc/288471

ER -

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