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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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On The Roman Domination Stable Graphs
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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Perfect Roman Domination and Unique Response Roman Domination [PDF]
arXiv.org, 2023 The idea of enumeration algorithms with polynomial delay is to polynomially bound the running time between any two subsequent solutions output by the enumeration algorithm.
Fernau, Henning, Mann, Kevin
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Signed Total Roman Domination in Digraphs
Discussiones Mathematicae Graph Theory, 2017 Let D be a finite and simple digraph with vertex set V (D). A signed total Roman dominating function (STRDF) on a digraph D is a function f : V (D) → {−1, 1, 2} satisfying the conditions that (i) ∑x∈N−(v)f(x) ≥ 1 for each v ∈ V (D), where N−(v) consists ...
Volkmann Lutz
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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.
M. Chellali +3 more
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Roman domination in direct product graphs and rooted product graphs [PDF]
AIMS Mathematics, 2021 Let $ G $ be a graph with vertex set $ V(G) $. A function $ f:V(G)\rightarrow \{0, 1, 2\} $ is a Roman dominating function on $ G $ if every vertex $ v\in V(G) $ for which $ f(v) = 0 $ is adjacent to at least one vertex $ u\in V(G) $ such that $ f(u) = 2
Abel Cabrera Martínez +2 more
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Further Results on the Total Roman Domination in Graphs [PDF]
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 ...
Abel Cabrera Martínez +2 more
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Edge Roman domination on graphs [PDF]
Graphs and Combinatorics, 2014 An edge Roman dominating function of a graph $G$ is a function $f\colon E(G) \rightarrow \{0,1,2\}$ satisfying the condition that every edge $e$ with $f(e)=0$ is adjacent to some edge $e'$ with $f(e')=2$.
Chang, Gerard J. +2 more
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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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On the Roman domination number of a graph
Discrete Mathematics, 2008 AbstractA Roman dominating function of a graph G is a labeling f:V(G)⟶{0,1,2} such that every vertex with label 0 has a neighbor with label 2. The Roman domination number γR(G) of G is the minimum of ∑v∈V(G)f(v) over such functions. A Roman dominating function of G of weight γR(G) is called a γR(G)-function.
Odile Favaron +3 more
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