Results 31 to 40 of about 1,279 (174)
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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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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On the Roman Edge Domination Number of a Graph [PDF]
, 2010 Let G be a simple graph with vertex set V (G) and edge set E(G)
K. Ebadi +5 more
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On trees with equal Roman domination and outer-independent Roman domination number [PDF]
Communications in Combinatorics and Optimization, 2019 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 $f(v) = 2$.
S. Nazari-Moghaddam, S.M. Sheikholeslami
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A note on the Roman domatic number of a digraph [PDF]
Communications in Combinatorics and Optimization, 2020 A {\em Roman dominating function} on a digraph $D$ with vertex set $V(D)$ is a labeling $f\colon V(D)\to \{0, 1, 2\}$ such that every vertex with label $0$ has an in-neighbor with label $2$. A set $\{f_1,f_2,\ldots,f_d\}$ of Roman dominating functions
Lutz Volkmann, D. Meierling
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Double Roman reinforcement number in graphs
AKCE International Journal of Graphs and Combinatorics, 2021 For a graph a double Roman dominating function is a function having the property that if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, and if f(v) = 1, then vertex v must have at least one ...
J. Amjadi, H. Sadeghi
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Minimal Roman Dominating Function
International Journal of Mathematics and Soft Computing, 2017 In this paper, the concept of Minimal Roman Dominating Function is considered. A characterization of a Minimal Roman Dominating Function has been given. It has also been proved that for any graph with vertices, the Upper Roman Domination Number is . It is also shown that if is a Minimal Roman Dominating Function then is a Roman Dominating Function for ...
Sanket Mukundbhai Badiyani +1 more
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THE ROMAN BONDAGE NUMBER OF A DIGRAPH [PDF]
, 2016 Let D=(V,A)D=(V,A) be a finite and simple digraph. A Roman dominating function on DD is a labeling f:V(D)→{0,1,2}f:V(D)→{0,1,2} such that every vertex with label 0 has an in-neighbor with label 2.
Sheikholeslami, Seyed Mahmoud;Dehgardi, Nasrin;Volkmann, Lutz;Meierling, Dirk +4 more
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Strong equality of Roman and perfect Roman Domination in trees [PDF]
, 2022 A Roman dominating function (RD-function) 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.
Hadi Rahbani +4 more
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Roman dominating influence parameters [PDF]
, 2006 A function f: V (G) → {0,1,2} is a Roman dominating function for a graph G = (V,E) if for every vertex v with f(v) = 0, there exists a vertex w ∈ N(v) with f(w) = 2. Emperor Constantine had the requirement that an army or legion could be sent from its
Peter J. Slater +3 more
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