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Discussiones Mathematicae. Graph Theory, ISSN 2083-5892, 2019, Volume 39, Issue 2, pp. 519 - 532
.... The weight of a total Roman dominating function is the value ( )) = Σ f ( ). The ) is the minimum weight of a total Roman dominating function of . Ahangar in [H.A... 
total Roman domination number | 05C69 | total Roman dominating function | trees | MATHEMATICS
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 10/2016, Volume 32, Issue 3, pp. 855 - 871
Let $$G$$ G be a finite and simple graph with vertex set $$V(G)$$ V ( G ) . A signed total Roman dominating function (STRDF) on a graph $$G$$ G is a function $$f:V(G)\rightarrow \{-1,1,2\}$$ f : V ( G ) → { - 1 , 1 , 2... 
Convex and Discrete Geometry | Total dominating set | Total domination number | Signed total Roman dominating function | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | 05C69 | Optimization | Signed total Roman domination number | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Journal Article
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 11/2017, Volume 37, Issue 4, pp. 1039 - 1053
Journal Article
Journal of combinatorial optimization, ISSN 1573-2886, 2017, Volume 35, Issue 1, pp. 126 - 133
Journal Article
Discussiones Mathematicae. Graph Theory, ISSN 2083-5892, 2017, Volume 37, Issue 1, pp. 261 - 272
Let be a finite and simple digraph with vertex set ( ). A signed total Roman dominating function (STRDF... 
05C20 | signed total Roman dominating function | 05C69 | digraph | signed total Roman domination number | Digraph | Signed total Roman domination number | Signed total Roman dominating function | MATHEMATICS | GRAPHS
Journal Article
Asian-European journal of mathematics, ISSN 1793-5571, 06/2018, Volume 11, Issue 3
Journal Article
Discussiones Mathematicae. Graph Theory, ISSN 1234-3099, 2017, Volume 37, Issue 4, pp. 1027 - 1038
Let k ≥ 1 be an integer. A signed total Roman k-dominating function on a graph G is a function f : V (G) → {−1, 1, 2} such that Ʃ f(u) ≥ k for every v ∈ V (G), where N(v... 
signed total Roman k-domatic number | signed total Roman k-domination number | signed total Roman k-dominating function | Signed total Roman k-domatic number | Signed total Roman k-domination number | Signed total Roman k-dominating function | MATHEMATICS | DOMINATION
Journal Article
Discrete mathematics, algorithms, and applications, ISSN 1793-8309, 04/2018, Volume 10, Issue 2
Journal Article
Journal of combinatorial optimization, ISSN 1573-2886, 2019, Volume 39, Issue 3, pp. 747 - 763
A function f:V(G)->{0,1,2} is a Roman dominating function (RDF) if every vertex u for which f(u... 
MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Dominating set | Total dominating set | 3-SAT | Total Roman dominating function | Algorithm
Journal Article
Mathematics (Basel), ISSN 2227-7390, 08/2020, Volume 8, Issue 9, p. 1438
Given a graph G without isolated vertices, a total Roman dominating function for G is a function f:V(G)→{0,1,2... 
Lower bounds | Graphs | Mathematical functions | Graph theory | Apexes | Roman civilization | direct product graphs | Roman domination | total Roman domination
Journal Article
Ars combinatoria, ISSN 0381-7032, 04/2020, Volume 150, pp. 225 - 240
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... 
MATHEMATICS | total Roman domination number | total Roman dominating function
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 12/2016, Volume 214, pp. 179 - 186
A signed total Roman dominating function on a graph G is a function f:V(G)⟶{−1,1,2} such that ∑u∈N(v)f(u)≥1 for every vertex v... 
Signed total Roman domatic number | Signed total Roman domination number | Signed total Roman dominating function | MATHEMATICS, APPLIED
Journal Article
Applicable analysis and discrete mathematics, ISSN 1452-8630, 10/2016, Volume 10, Issue 2, pp. 501 - 517
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... 
Leaves | Literature | Mathematical theorems | Cardinality | Double stars | Discrete mathematics | Mathematical functions | Graph theory | Mathematical minima | Vertices | Roman domination | Total Roman domination | Total domination | Domina-tion | Domination | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Journal of Combinatorial Mathematics and Combinatorial Computing, ISSN 0835-3026, 05/2018, Volume 105, pp. 105 - 116
Journal Article
Communications in combinatorics and optimization, ISSN 2538-2128, 06/2016, Volume 1, Issue 2, pp. 165 - 178
...$-dominating function (STR$k$DF) on‎ ‎$D$ is a function $f:V(D)\rightarrow\{-1‎, ‎1‎, ‎2\}$ satisfying the conditions‎ ‎that (i) $\sum_{x\in N^{-}(v)}f(x)\ge k$ for each‎ ‎$v\in V(D)$‎, ‎where $N^{-}(v... 
Digraph | Signed total Roman $k$-domination | Signed total Roman $k$-dominating function
Journal Article
Iranian Journal of Science and Technology, Transactions A: Science, ISSN 1028-6276, 6/2018, Volume 42, Issue 2, pp. 841 - 846
Journal Article
Resultate der Mathematik, ISSN 1420-9012, 2019, Volume 74, Issue 4, pp. 1 - 18
A quasi-total Roman dominating function on a graph $$G=(V, E)$$ G=(V,E) is a function $$f : V \rightarrow \{0,1,2\}$$ f:V→{0,1,2} satisfying... 
Mathematics, general | Mathematics | Quasi-total Roman domination number | Roman domination number | total Roman domination number | 05C69 | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2019, Volume 263, pp. 257 - 270
...)=0 for every vertex u adjacent to v. We call the function f a weak Roman dominating function if for every v such that f(v... 
Lexicographic product | Domination in graphs | Total domination | Weak roman domination | Double total domination | MATHEMATICS, APPLIED | Minimum weight | Graphs | Mathematical functions | Apexes | Invariants
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 06/2019, Volume 263, pp. 88 - 95
A total Roman dominating function of a graph G=(V,E) is a function f:V(G)→{0,1,2} such that for every vertex v with f... 
Roman domination | Total Roman domination | Lexicographic product graphs | MATHEMATICS, APPLIED | NUMBER | Graphs | Mathematical functions | Graph theory | Apexes
Journal Article
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