Results 11 to 20 of about 14,901,088 (199)
Total Roman Domination Number of Rooted Product Graphs [PDF]
Mathematics, 2020 Let G be a graph with no isolated vertex and f:V(G)→{0,1,2} a function. If f satisfies that every vertex in the set {v∈V(G):f(v)=0} is adjacent to at least one vertex in the set {v∈V(G):f(v)=2}, and if the subgraph induced by the set {v∈V(G):f(v)≥1} has ...
Abel Cabrera Martínez +3 more
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Closed formulas for the total Roman domination number of lexicographic product graphs [PDF]
Ars Mathematica Contemporanea, 2021 Let G be a graph with no isolated vertex and f: V(G) → {0, 1, 2} a function. Let Vi = {x ∈ V(G) : f(x) = i} for every i ∈ {0, 1, 2}. We say that f is a total Roman dominating function on G if every vertex in V0 is adjacent to at least one vertex in V2 and the subgraph induced by V1 ∪ V2 has no isolated vertex.
Abel Cabrera Martínez +1 more
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Relating the Outer-Independent Total Roman Domination Number with Some Classical Parameters of Graphs [PDF]
Mediterranean Journal of Mathematics, 2022 AbstractFor a given graph G without isolated vertex we consider a function $$f: V(G) \rightarrow \{0,1,2\}$$ f : V ( G ) → { 0 ,
Abel Cabrera Martínez +2 more
openaire +5 more sources
Total Roman domination for proper interval graphs
Electronic Journal of Graph Theory and Applications, 2020 A function f:V → {0,1,2} is a total Roman dominating function (TRDF) on a graph G=(V,E) if for every vertex v ∈ V with f(v) = 0 there is a vertex u adjacent to v with f(u) = 2 and for every vertex v ∈ V with f(v) > 0 there exists a vertex u ∈ NG(v ...
Abolfazl Poureidi
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Signed Total Roman Domination in Digraphs [PDF]
Discussiones Mathematicae Graph Theory, 2017 Let D be a finite and simple digraph with vertex set V (D). A signed total Roman dominating function (STRDF) on a digraph D is a function f : V (D) → {−1, 1, 2} satisfying the conditions that (i) ∑x∈N−(v)f(x) ≥ 1 for each v ∈ V (D), where N−(v) consists ...
Volkmann Lutz
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On The Total Roman Domination in Trees [PDF]
Discussiones Mathematicae Graph Theory, 2019 A total Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the following conditions: (i) every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2 and (ii) the subgraph of G induced by ...
Amjadi Jafar +2 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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Signed Total Roman Edge Domination In Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2017 Let G = (V,E) be a simple graph with vertex set V and edge set E. A signed total Roman edge dominating function of G is a function f : Ʃ → {−1, 1, 2} satisfying the conditions that (i) Ʃe′∈N(e) f(e′) ≥ 1 for each e ∈ E, where N(e) is the open ...
Asgharsharghi Leila +1 more
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On the outer-independent total (Roman) domination number of some graph operators
RAIRO - Operations ResearchThe goal of this article is to obtain closed formulas for the outer-independent total domina- tion number and the outer-independent total Roman domination number of the following well-known graph operators defined from a connected graph G : the central graph C(G)
Ismael Rios-Villamar +2 more
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From Total Roman Domination in Lexicographic Product Graphs to Strongly Total Roman Domination in Graphs [PDF]
, 2021 [EN] Let G be a graph with no isolated vertex and let N (v) be the open neighbourhood of v is an element of V (G). Let f : V (G) -> {0, 1, 2} be a function and V-i = {v is an element of V (G) : f (v) = i} for every i is an element of{0, 1, 2}.
Ana Almerich-Chulia +7 more
core +2 more sources