Results 11 to 20 of about 128,488 (305)
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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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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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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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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Edge Roman Domination on Graphs [PDF]
Graphs and Combinatorics, 2016 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 $f(e')=2$. The edge Roman domination number of $G$, denoted by $γ'_R(G)$, is the minimum weight $w(f) = \sum_{e\in E(G)} f(e)$ of an edge Roman dominating ...
Gerard J. Chang +2 more
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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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Perfect Domination, Roman Domination and Perfect Roman Domination in Lexicographic Product Graphs
Fundamenta Informaticae, 2022 The aim of this paper is to obtain closed formulas for the perfect domination number, the Roman domination number and the perfect Roman domination number of lexicographic product graphs. We show that these formulas can be obtained relatively easily for the case of the first two parameters.
Cabrera Martínez, A. +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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