Results 31 to 40 of about 708,300 (289)
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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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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Total Roman {2}-Dominating Functions in Graphs
Discussiones Mathematicae Graph Theory, 2022 A Roman {2}-dominating function (R2F) is a function f : V → {0, 1, 2} with the property that for every vertex v ∈ V with f(v) = 0 there is a neighbor u of v with f(u) = 2, or there are two neighbors x, y of v with f(x) = f(y) = 1.
Ahangar H. Abdollahzadeh +3 more
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Critical graphs with Roman domination number four
AKCE International Journal of Graphs and Combinatorics, 2020 A Roman domination function on a graph G is a function satisfying the condition that every vertex u for which r(u) = 0 is adjacent to at least one vertex v for which r(v) = 2.
A. Martínez-Pérez, D. Oliveros
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Discrete Mathematics, 2004 The paper studies the Roman domination in graphs. It is a special kind of domination whose introduction was motivated by military rules of the ancient Roman Empire. Let \(G\) be a graph with vertex set \(V(G)\), and let \(f: V(G)\to \{0,1,2\}\). If to each vertex \(v\) with \(f(v)= 0\) there exists a vertex \(w\) with \(f(w)= 2\) adjacent to \(v ...
Ernest J. Cockayne +3 more
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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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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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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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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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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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