On The Roman Domination Stable Graphs

Majid 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 -