Results 31 to 40 of about 302 (207)
A characterization of trees with equal Roman 2-domination and Roman domination numbers
Communications in Combinatorics and Optimization, 2019 Summary: 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 \(V_i=\{v\in V :f(v)=i\}\), for \(i=0,1,2\).
Gonzalez Yero, Ismael +1 more
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On the roman domination number of generalized Sierpiński graphs [PDF]
Filomat, 2017 A map f : V?(0,1,2) is a Roman dominating function on a graph G = (V,E) if for every vertex v ? V with f(v)=0, there exists a vertex u, adjacent to v, such that f(u)=2. The weight of a Roman dominating function is given by f(V)=?u?V f(u). The minimum weight among all Roman dominating functions on G is called the Roman domination number of G.
Ramezani, F. +2 more
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On trees with equal Roman domination and outer-independent Roman domination numbers
Communications in Combinatorics and Optimization, 2019 Summary: A Roman dominating function (RDF) on a graph \(G\) is a function \(f : V (G) \to \{0, 1, 2\}\) satisfying the condition that every vertex \(u\) for which \(f(u) = 0\) is adjacent to at least one vertex \(v\) for which \(f(v) = 2\). A Roman dominating function \(f\) is called an outer-independent Roman dominating function (OIRDF) on \(G\) if ...
Sheikholeslami, Seyed Mahmoud +1 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. The weight of an RDF is the value f(V (G)) = P u2V (G) f(u). An RDF f in a graph G is independent if no two vertices assigned positive values are
Mustapha Chellali, Nader Jafari Rad
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Discussiones Mathematicae Graph Theory, 2022 A 2-rainbow dominating function (2RDF) of a graph G is a function g from the vertex set V (G) to the family of all subsets of {1, 2} such that for each vertex v with g(v) =∅ we have ∪u∈N(v) g(u) = {1, 2}.
Poureidi Abolfazl, Rad Nader Jafari
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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 the total Roman domination stability in graphs
AKCE International Journal of Graphs and Combinatorics, 2021 A total Roman dominating function on a graph G is a function satisfying the conditions: (i) every vertex u with f(u) = 0 is adjacent to at least one vertex v of G for which f(v) = 2; (ii) the subgraph induced by the vertices assigned non-zero values has ...
Ghazale Asemian +3 more
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Roman {2}-Bondage Number of a Graph
Discussiones Mathematicae Graph Theory, 2020 For a given graph G=(V, E), a Roman {2}-dominating function f : V (G) → {0, 1, 2} has the property that for every vertex u with f(u) = 0, either u is adjacent to a vertex assigned 2 under f, or is adjacent to at least two vertices assigned 1 under f. The
Moradi Ahmad +2 more
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Bounds on the Double Italian Domination Number of a Graph
Discussiones Mathematicae Graph Theory, 2022 For a graph G, a Roman {3}-dominating function is a function f : V → {0, 1, 2, 3} having the property that for every vertex u ∈ V, if f(u) ∈ {0, 1}, then f(N[u]) ≥ 3.
Azvin Farzaneh, Rad Nader Jafari
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Calculating Modern Roman Domination of Fan Graph and Double Fan Graph [PDF]
Journal of Applied Sciences and Nanotechnology, 2022 This paper is concerned with the concept of modern Roman domination in graphs. A Modern Roman dominating function on a graph is labeling such that every vertex with label 0 is adjacent to two vertices; one of them of label 2 and the other of label 3 and ...
Saba Salah, Ahmed Omran, Manal Al-Harere
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