Results 11 to 20 of about 708,300 (289)

Triple Roman domination in graphs

Applied Mathematics and Computation, 2021
The Roman domination in graphs is well-studied in graph theory. The topic is related to a defensive strategy problem in which the Roman legions are settled in some secure cities of the Roman Empire. The deployment of the legions around the Empire is designed in such a way that a sudden attack to any undefended city could be quelled by a legion from a ...
Mustapha Chellali, H Abdollahzadeh Ahangar, S M Sheikholeslami   +2 more
exaly   +4 more sources

Roman Domination of Cartesian Bundles of Cycles over Cycles

Mathematics
A Roman dominating function f of a graph G=(V,E) assigns labels from the set {0,1,2} to vertices such that every vertex labeled 0 has a neighbor labeled 2. The weight of an RDF f is defined as w(f)=∑v∈Vf(v), and the Roman domination number, γR(G), is the
Simon Brezovnik, Janez Žerovnik
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On the double Roman domination in graphs

Discrete Applied Mathematics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hossein Abdollahzadeh Ahangar, Seyed Mahmoud Sheikholeslami   +1 more
exaly   +3 more sources

More results on the signed double Roman domination number of graphs

AKCE International Journal of Graphs and Combinatorics
A signed double Roman dominating function (SDRD-function) on a graph G is defined as a function [Formula: see text] having the property that [Formula: see text] for each [Formula: see text] and if [Formula: see text], then the vertex u must have a ...
Seyed Mahmoud Sheikholeslami, Lutz Volkmann   +1 more
doaj   +2 more sources

Perfect Roman Domination: Aspects of Enumeration and Parameterization

Algorithms
Perfect Roman Dominating Functions and Unique Response Roman Dominating Functions are two ways to translate perfect code into the framework of Roman Dominating Functions.
Kevin Mann, Henning Fernau
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Strong Equality Between the Roman Domination and Independent Roman Domination Numbers in Trees

Discussiones Mathematicae Graph Theory, 2013
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.
Chellali Mustapha, Rad Nader Jafari
doaj   +2 more sources

On the Total Double Roman Domination [PDF]

IEEE Access, 2019
Let G = (V, E) be a simple graph. A double Roman dominating function (DRDF) on G is a function f from the vertex set V of G into {0, 1, 2, 3} such that if f (u) = 0, then u must have at least two neighbors assigned 2 or one neighbor assigned 3 under f ...
Zehui Shao, Jafar Amjadi, Seyed Mahmoud Sheikholeslami, Mina Valinavaz   +3 more
doaj   +2 more sources

Quasi total double Roman domination in graphs

AKCE International Journal of Graphs and Combinatorics
A quasi total double Roman dominating function (QTDRD-function) on a graph [Formula: see text] is a function [Formula: see text] having the property that (i) if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w
S. Kosari, S. Babaei, J. Amjadi, M. Chellali, S. M. Sheikholeslami   +4 more
doaj   +2 more sources

On the Roman domination number of a graph

Discrete Mathematics, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rana Khoeilar, H Karami, S M Sheikholeslami   +2 more
exaly   +3 more sources

Some Results on the Strong Roman Domination Number of Graphs [PDF]

Mathematics Interdisciplinary Research, 2020
Let G=(V,E) be a finite and simple graph of order n and maximum‎ ‎degree Δ(G)‎. ‎A strong Roman dominating function on a‎ ‎graph  G  is a function  f‎:V (G)→{0‎, ‎1,… ,‎[Δ(G)/2 ]‎+ ‎1}  satisfying the condition that every‎ ‎vertex v for which  f(v)=0  is
Akram Mahmoodi, Sakineh Nazari-Moghaddam, Afshin Behmaram   +2 more
doaj   +1 more source