Results 41 to 50 of about 152,920 (311)
The Roman domination and domatic numbers of a digraph [PDF]
Communications in Combinatorics and Optimization, 2019 Let $D$ be a simple digraph with vertex set $V$. A Roman dominating function (RDF) on a digraph $D$ is a function $f: V\rightarrow \{0,1,2\}$ satisfying the condition that every vertex $v$ with $f(v)=0$ has an in-neighbor $u$ with $f(u)=2$. The weight
Z.Xie1, G. Hao, Sh. Wei
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Domination parameters with number 2: Interrelations and algorithmic consequences [PDF]
, 2018 In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied invariants: the weak 2-domination ...
Bonomo, Flavia +4 more
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On the signed strong total Roman domination number of graphs
Tamkang Journal of Mathematics, 2022 Let $G=(V,E)$ be a finite and simple graph of order $n$ and maximumdegree $\Delta$. A signed strong total Roman dominating function ona graph $G$ is a function $f:V(G)\rightarrow\{-1, 1,2,\ldots, \lceil\frac{\Delta}{2}\rceil+1\}$ satisfying the condition
A. Mahmoodi, M. Atapour, S. Norouzian
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Bounds on the Global Double Roman Domination Number in Graphs
Discussiones Mathematicae Graph Theory, 2022 Let G be a simple graph of order n and let γgdR(G) be the global double Roman domination number of G. In this paper, we give some upper bounds on the global double Roman domination number of G.
Guoliang Hao +3 more
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Strong Equality of Perfect Roman and Weak Roman Domination in Trees [PDF]
, 2019 Let G=(V,E) be a graph and f:V⟶{0,1,2} be a function. Given a vertex u with f(u)=0, if all neighbors of u have zero weights, then u is called undefended with respect to f.
Alhevaz, Abdollah +3 more
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Relating the Outer-Independent Total Roman Domination Number with Some Classical Parameters of Graphs [PDF]
Mediterranean Journal of Mathematics, 2021 For a given graph G without isolated vertex we consider a function $$f: V(G) \rightarrow \{0,1,2\}$$ f : V ( G ) → { 0 , 1 , 2 } . For every $$i\in \{0,1,2\}$$ i ∈ { 0 , 1 , 2 } , let $$V_i=\{v\in V(G):\; f(v)=i\}$$ V i = { v ∈ V ( G ) : f ( v ) = i ...
A. Cabrera Martínez +2 more
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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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A note on the independent roman domination in unicyclic graphs [PDF]
, 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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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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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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