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Double Roman Domination: A Survey

Mathematics, 2023
Since 2016, when the first paper of the double Roman domination appeared, the topic has received considerable attention in the literature. We survey known results on double Roman domination and some variations of the double Roman domination, and a list ...
Darja Rupnik Poklukar, Janez Žerovnik
doaj   +5 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   +5 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   +4 more sources

Complexity of Roman {2}-domination and the double Roman domination in graphs [PDF]

AKCE International Journal of Graphs and Combinatorics, 2020
For a simple, undirected graph a Roman {2}-dominating function (R2DF) has the property that for every vertex with f(v) = 0, either there exists a vertex with f(u) = 2, or at least two vertices with The weight of an R2DF is the sum The minimum weight of ...
Chakradhar Padamutham, Venkata Subba Reddy Palagiri   +1 more
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Double Roman domination

Discrete Applied Mathematics, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Teresa W Haynes, Stephen T Hedetniemi
exaly   +4 more sources

On the double Roman domination in graphs

Discrete Applied Mathematics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hossein Abdollahzadeh Ahangar, Mustapha Chellali, S M Sheikholeslami   +2 more
exaly   +4 more sources

Independent double Roman domination in graphs [PDF]

AKCE International Journal of Graphs and Combinatorics, 2020
For a graph G = (V,E), a double Roman dominating function has the property that for every vertex with f(v) = 0, either there exists a vertex , with f(u) = 3, or at least two neighbors having f(x) = f(y) = 2, and every vertex with value 1 under f has at ...
H. R. Maimani, M. Momeni, F. Rahimi Mahid, S. M. Sheikholeslami   +3 more
doaj   +3 more sources

On the Outer-Independent Double Roman Domination of Graphs [PDF]

Frontiers in Applied Mathematics and Statistics, 2021
An outer-independent double Roman dominating function (OIDRDF) of a graph G is a function h:V(G)→{0,1,2,3} such that i) every vertex v with f(v)=0 is adjacent to at least one vertex with label 3 or to at least two vertices with label 2, ii) every vertex ...
Yongsheng Rao, Saeed Kosari, Seyed Mahmoud Sheikholeslami, M. Chellali, Mahla Kheibari   +4 more
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Some Progress on the Double Roman Domination in Graphs

Discussiones Mathematicae Graph Theory, 2019
For a graph G = (V,E), a double Roman dominating function (or just DRDF) is a function f : V → {0, 1, 2, 3} having the property that if f(v) = 0 for a vertex v, then v has at least two neighbors assigned 2 under f or one neighbor assigned 3 under f, and ...
Rad Nader Jafari, Rahbani Hadi
doaj   +3 more sources

Discharging Approach for Double Roman Domination in Graphs

IEEE Access, 2018
The discharging method is most well-known for its central role in the proof of the Four Color Theorem. This proof technique was extensively applied to study various graph coloring problems, in particular on planar graphs.
Zehui Shao, Pu Wu, Huiqin Jiang, Zepeng Li, Janez Zerovnik, Xiujun Zhang   +5 more
doaj   +4 more sources