Results 21 to 30 of about 1,370 (272)
On The Roman Domination Stable Graphs
Discussiones Mathematicae Graph Theory, 2017 A Roman dominating function (or just 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.
Hajian Majid, Rad Nader Jafari
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Roman game domination subdivision number of a graph [PDF]
Transactions on Combinatorics, 2013 A {em Roman dominating function} on a graph $G = (V ,E)$ is a function $f : Vlongrightarrow {0, 1, 2}$ satisfying the condition that every vertex $v$ for which $f (v) = 0$ is adjacent to at least one vertex $u$ for which $f (u) = 2$. The {em weight} of a
Jafar Amjadi +3 more
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Total Roman Reinforcement in Graphs
Discussiones Mathematicae Graph Theory, 2019 A total Roman dominating function on a graph G is a labeling f : V (G) → {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2 and the subgraph of G induced by the set of all vertices of positive weight has no isolated vertex.
Ahangar H. Abdollahzadeh +4 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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Minimal Roman Dominating Functions: Extensions and Enumeration
Algorithmica, 2022 AbstractRoman domination is one of the many variants of domination that keeps most of the complexity features of the classical domination problem. We prove that Roman domination behaves differently in two aspects: enumeration and extension. We develop non-trivial enumeration algorithms for minimal Roman dominating functions with polynomial delay and ...
Faisal N. Abu-Khzam +2 more
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Convex Roman Dominating Function in Graphs
European Journal of Pure and Applied Mathematics, 2023 Let $G$ be a connected graph. A function $f:V(G)\rightarrow \{0,1,2\}$ is a \textit{convex Roman dominating function} (or CvRDF) if every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$ and $V_1 \cup V_2$ is convex.
Rona Jane Fortosa, Sergio Canoy
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A Constructive Characterization of Vertex Cover Roman Trees
Discussiones Mathematicae Graph Theory, 2021 A Roman dominating function on a graph G = (V (G), E(G)) is a function f : V (G) → {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.
Martínez Abel Cabrera +2 more
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On Double Roman Dominating Functions in Graphs
European Journal of Pure and Applied Mathematics, 2023 Let G be a connected graph. A function f : V (G) → {0, 1, 2, 3} is a double Roman dominating function of G if for each v ∈ V (G) with f(v) = 0, v has two adjacent vertices u and w for which f(u) = f(w) = 2 or v has an adjacent vertex u for which f(u) = 3, and for each v ∈ V (G) with f(v) = 1, v is adjacent to a vertex u for which either f(u) = 2 or f(u)
Jerry Boy Cariaga, Ferdinand Jamil
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Total Protection of Lexicographic Product Graphs
Discussiones Mathematicae Graph Theory, 2022 Given a graph G with vertex set V (G), a function f : V (G) → {0, 1, 2} is said to be a total dominating function if Σu∈N(v) f(u) > 0 for every v ∈ V (G), where N(v) denotes the open neighbourhood of v. Let Vi = {x ∈ V (G) : f(x) = i}. A total dominating
Martínez Abel Cabrera +1 more
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Geodetic Roman Dominating Functions in a Graph
European Journal of Pure and Applied Mathematics, 2023 Let $G$ be a connected graph. A function $f: V(G)\rightarrow \{0,1,2\}$ is a \textit{geodetic Roman dominating function} (or GRDF) if every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$ and $V_1 \cup V_2$ is a geodetic set in $G$.
Rona Jane Gamayot Fortosa, Sergio Canoy
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