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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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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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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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A note on the independent roman domination in unicyclic graphs [PDF]
Opuscula Mathematica, 2012 A Roman dominating function (RDF) on a graph \(G = (V;E)\) is a function \(f : V \to \{0, 1, 2\}\) satisfying the condition that every vertex \(u\) for which \(f(u) = 0\) is adjacent to at least one vertex \(v\) for which \(f(v) = 2\).
Mustapha Chellali, Nader Jafari Rad
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Restrained roman domination in graphs [PDF]
Transactions on Combinatorics, 2015 A Roman dominating function (RDF) on a graph G = (V,E) is defined to be a function 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. A set S V is a Restrained dominating set if every
Roushini Leely Pushpam +1 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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Strong Equality Between the Roman Domination and Independent Roman Domination Numbers in Trees
Discussiones Mathematicae Graph Theory, 2013 A Roman dominating function (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.
Chellali Mustapha, Rad Nader Jafari
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Vertex-Edge Roman Domination [PDF]
Kragujevac Journal of Mathematics, 2021 A vertex-edge Roman dominating function (or just ve-RDF) of a graph G = (V,E) is a function f : V (G) →{0, 1, 2} such that for each edge e = uv either max{f(u),f(v)}≠0 or there exists a vertex w such that either wu ∈ E or wv ∈ E and f(w) = 2. The weight of a ve-RDF is the sum of its function values over all vertices.
Kumar, H. Naresh, Venkatakrishnan, Y. B.
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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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