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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
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Survey on Roman {2}-Domination
MathematicsThe notion of Roman {2}-domination was introduced in 2016 as a variant of Roman domination, a concept inspired by a defending strategy used by the emperor Constantine (272–337 AD) to protect the Roman Empire.
Ahlam Almulhim +2 more
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Perfect Roman Domination: Aspects of Enumeration and Parameterization
AlgorithmsPerfect 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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Several Roman domination graph invariants on Kneser graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 This paper considers the following three Roman domination graph invariants on Kneser graphs: Roman domination, total Roman domination, and signed Roman domination.
Tatjana Zec, Milana Grbić
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Varieties of Roman domination IV
AKCE International Journal of Graphs and CombinatoricsRoman domination was introduced in 2004 by Cockayne, Dreyer, Hedetniemi, and Hedetniemi. If [Formula: see text] is the vertex set of a graph G, then a function [Formula: see text] is a Roman dominating function if every vertex [Formula: see text] for ...
M. Chellali +3 more
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Roman Domination of Cartesian Bundles of Cycles over Cycles
MathematicsA 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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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 +2 more
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Total double Roman domination in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:V\rightarrow\{0,1,2,3\}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one ...
Guoliang Hao +2 more
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On the Quasi-Total Roman Domination Number of Graphs
Mathematics, 2021 Domination theory is a well-established topic in graph theory, as well as one of the most active research areas. Interest in this area is partly explained by its diversity of applications to real-world problems, such as facility location problems ...
Abel Cabrera Martínez +2 more
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On [k] -Roman domination in graphs
AKCE International Journal of Graphs and Combinatorics, 2023 For an integer [Formula: see text] let f be a function that assigns labels from the set [Formula: see text] to the vertices of a simple graph [Formula: see text].
N. Khalili +3 more
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