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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
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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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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
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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
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Double Roman and double Italian domination [PDF]

Discussiones Mathematicae Graph Theory, 2023
Lutz Volkmann
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On the Double Roman Domination in Generalized Petersen Graphs P(5k,k) [PDF]

Mathematics, 2022
A double Roman dominating function on a graph G=(V,E) is a function f:V→{0,1,2,3} satisfying the condition that every vertex u for which f(u)=0 is adjacent to at least one vertex assigned 3 or at least two vertices assigned 2, and every vertex u with f(u)
Darja Rupnik Poklukar, Janez Žerovnik
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Bounds on the global double Roman domination number in graphs [PDF]

Discussiones Mathematicae Graph Theory, 2022
Guoliang Hao, Shouliu Wei, Seyed Mahmoud Sheikholeslami, Xiaodan Chen   +3 more
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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
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Bounds on the Double Italian Domination Number of a Graph

Discussiones Mathematicae Graph Theory, 2022
For a graph G, a Roman {3}-dominating function is a function f : V → {0, 1, 2, 3} having the property that for every vertex u ∈ V, if f(u) ∈ {0, 1}, then f(N[u]) ≥ 3.
Azvin Farzaneh, Rad Nader Jafari
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On the D-differential of a graph

AKCE International Journal of Graphs and Combinatorics, 2022
Let [Formula: see text] be a graph of order n(G). For a subset S of V(G), the boundary of S is defined as [Formula: see text] where N(S) is the open neighborhood of S.
Kijung Kim
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