Results 31 to 40 of about 129,618 (274)
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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Total Roman domination subdivision number in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 A {\em Roman dominating function} on a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2\}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$.
Jafar Amjad
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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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A note on Roman domination of digraphs
Discussiones Mathematicae Graph Theory, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen Xiaodan, Hao Guoliang, Xie Zhihong
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Graphs with Large Hop Roman Domination Number [PDF]
Computer Science Journal of Moldova, 2019 A subset $S$ of vertices of a graph $G$ is a hop dominating set if every vertex outside $S$ is at distance two from a vertex of $S$. A Roman dominating function on a graph $G=(V,E)$ is a function $f: V(G) \longrightarrow \{0, 1, 2\}$ satisfying the ...
E. Shabani, N. Jafari Rad, A. Poureidi
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Roman Domination in Complementary Prism Graphs [PDF]
, 2012 A Roman domination function on a complementary prism graph GGc is a function f : V [ V c ! {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2. The Roman domination number R(GGc) of a graph G = (V,E) is the minimum of Px2V [V c f(x)
Chaitra, V., Chaluvaraju, B.
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[k]-Roman Domination in Digraphs
Symmetry, 2023 Let D=(V(D),A(D)) be a finite, simple digraph and k a positive integer. A function f:V(D)→{0,1,2,…,k+1} is called a [k]-Roman dominating function (for short, [k]-RDF) if f(AN−[v])≥|AN−(v)|+k for any vertex v∈V(D), where AN−(v)={u∈N−(v):f(u)≥1} and AN−[v]=AN−(v)∪{v}. The weight of a [k]-RDF f is ω(f)=∑v∈V(D)f(v).
Xinhong Zhang, Xin Song, Ruijuan Li
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On the co-Roman domination in graphs
Discussiones Mathematicae Graph Theory, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zehui Shao +4 more
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Roman domination in oriented trees [PDF]
Electronic Journal of Graph Theory and Applications, 2021 Summary: Let \(D=(V,A)\) be a digraph of order \(n= |V|\). A \textit{Roman dominating function} of a digraph \(D\) is a function \(f: V \rightarrow \{0,1,2\}\) such that every vertex \(u\) for which \(f(u) = 0\) has an in-neighbor \(v\) for which \(f(v) = 2\). The weight of a \textit{Roman dominating function} is the value \(f(V)= \sum_{u \in V }f(u)\).
Lyes Ouldrabah +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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