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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 ...
Janez Žerovnik, Darja Rupnik Poklukar
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Varieties of Roman domination II [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 In this work, we continue to survey what has been done on the Roman domination. More precisely, we will present in two sections several variations of Roman dominating functions as well as the signed version of some of these functions.
Mustapha Chellali +2 more
exaly +6 more sources
Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Teresa Haynes, Stephen T Hedetniemi
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On The Roman Domination Stable Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2017 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.
Hajian Majid, Rad Nader Jafari
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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 +1 more
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Relating 2-Rainbow Domination To Roman Domination
Discussiones Mathematicae Graph Theory, 2017 For a graph G, let R(G) and yr2(G) denote the Roman domination number of G and the 2-rainbow domination number of G, respectively. It is known that yr2(G) ≤ R(G) ≤ 3/2yr2(G). Fujita and Furuya [Difference between 2-rainbow domination and Roman domination
Alvarado José D. +2 more
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Independent roman $\{3\}$-domination [PDF]
Transactions on Combinatorics, 2022 Let $G$ be a simple, undirected graph. In this paper, we initiate the study of independent Roman $\{3\}$-domination. A function $g : V(G) \rightarrow \lbrace 0, 1, 2, 3 \rbrace$ having the property that $\sum_{v \in N_G(u)}^{} g(v) \geq 3$, if $g(u) = 0$,
P. Chakradhar, P. Venkata Subba Reddy
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Further Results on the Total Roman Domination in Graphs
Mathematics, 2020 Let G be a graph without isolated vertices. A function f : V ( G ) → { 0 , 1 , 2 } is a total Roman dominating function on G if every vertex v ∈ V ( G ) for which f ( v ) = 0 is adjacent to at least one vertex u ...
Andres Carrión Garcia +2 more
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A characterization of trees with equal Roman $\{2\}$-domination and Roman domination numbers [PDF]
Communications in Combinatorics and Optimization, 2019 Given a graph $G=(V,E)$ and a vertex $v \in V$, by $N(v)$ we represent the open neighbourhood of $v$. Let $f:V\rightarrow \{0,1,2\}$ be a function on $G$. The weight of $f$ is $\omega(f)=\sum_{v\in V}f(v)$ and let $V_i=\{v\in V \colon f(v)=i\}$, for $i=0,
Abel Cabrera Martinez, Ismael G. Yero
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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 ...
H Abdollahzadeh Ahangar
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