Results 11 to 20 of about 700 (247)
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
doaj +3 more sources
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
openaire +7 more sources
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 +6 more sources
Total Roman {2}-Dominating Functions in Graphs [PDF]
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
doaj +4 more sources
Total Roman domination for proper interval graphs [PDF]
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
doaj +2 more sources
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
doaj +2 more sources
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
doaj +2 more sources
Total Roman domination on the digraphs [PDF]
Open Mathematics, 2023 Let D=(V,A)D=\left(V,A) be a simple digraph with vertex set VV, arc set AA, and no isolated vertex. A total Roman dominating function (TRDF) of DD is a function h:V→{0,1,2}h:V\to \left\{0,1,2\right\}, which satisfies that each vertex x∈Vx\in V with h(x ...
Zhang Xinhong, Song Xin, Li Ruijuan
doaj +2 more sources
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
doaj +2 more sources
Total Roman Reinforcement in Graphs [PDF]
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
doaj +2 more sources