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Total Roman domination in graphs
Applicable Analysis and Discrete Mathematics, 2016 A Roman dominating function on a graph 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. The weight of a Roman dominating function f is the sum, ΣuV(G) f(u), of the weights of the vertices.
Hossein Ahangar Abdollahzadeh +3 more
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A characterization relating domination, semitotal domination and total Roman domination in trees [PDF]
, 2021 Summary: A total Roman dominating function on a graph \(G\) is a function \(f: V(G)\rightarrow\{0,1,2\}\) such that for every vertex \(v\in V(G)\) with \(f(v)=0\) there exists a vertex \(u\in V(G)\) adjacent to \(v\) with \(f(u)=2\), and the subgraph induced by the set \(\{x\in V(G): f(x)\geq 1\}\) has no isolated vertices.
Abel Cabrera Martínez +2 more
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Signed total strong Roman domination in graphs [PDF]
Discrete Mathematics Letters, 2022 Maryam Hajjari +1 more
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Total Perfect Roman Domination [PDF]
Symmetry, 2023 A total perfect Roman dominating function (TPRDF) on a graph G=(V,E) is a function f from V to {0,1,2} satisfying (i) every vertex v with f(v)=0 is a neighbor of exactly one vertex u with f(u)=2; in addition, (ii) the subgraph of G that is induced by the vertices with nonzero weight has no isolated vertex. The weight of a TPRDF f is ∑v∈Vf(v). The total
Ahlam Almulhim
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Nonnegative signed total Roman domination in graphs
Communications in Combinatorics and Optimization, 2020 Let $G$ be a finite and simple graph with vertex set $V(G)$. A nonnegative signed total Roman dominating function (NNSTRDF) on a graph $G$ is a function $f:V(G)\rightarrow\{-1, 1, 2\}$ satisfying the conditions that (i) $\sum_{x\in N(v)}f(x)\ge 0$ for
Nasrin Dehgardi, Lutz Volkmann
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Algorithmic Aspects of Quasi-Total Roman Domination in Graphs [PDF]
, 2022 Summary: For a simple, undirected, connected graph \(G(V,E)\), a function \(f : V(G) \rightarrow \{0,1,2\}\) which satisfies the following conditions is called a quasi-total Roman dominating function (QTRDF) of \(G\) with weight \(f(V(G))= \sum_{v \in V(G)} f(v)\).
P. Venkata Subba Reddy, Mangal Vikas
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Total Roman {2}-domination in graphs [PDF]
Quaestiones Mathematicae, 2019 23 ...
Suitberto Cabrera García +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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Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees [PDF]
Mathematics, 2021 For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v ...
Xinyue Liu +3 more
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Total Roman {3}-domination in Graphs [PDF]
Symmetry, 2020 For a graph G = ( V , E ) with vertex set V = V ( G ) and edge set E = E ( G ) , a Roman { 3 } -dominating function (R { 3 } -DF) is a function f : V ( G ) → { 0 , 1 , 2 , 3 } having the property that ∑ u ∈ N G ( v ) f ( u ) ≥ 3 , if f ( v ) = 0 , and ∑ u ∈ N G ( v ) f ( u
Zehui Shao +2 more
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