# On The Roman Domination Stable Graphs

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

top

## Abstract

top
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].

## How to cite

top

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].},
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
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 -

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.