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Journal of combinatorial optimization, ISSN 1573-2886, 2017, Volume 35, Issue 1, pp. 126 - 133
Journal Article
Resultate der Mathematik, ISSN 1420-9012, 2019, Volume 74, Issue 4, pp. 1 - 18
...) . The minimum weight of a quasi-total Roman dominating function on a graph G is called the quasi-total Roman domination number of G... 
Mathematics, general | Mathematics | Quasi-total Roman domination number | Roman domination number | total Roman domination number | 05C69 | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Applicable analysis and discrete mathematics, ISSN 1452-8630, 10/2016, Volume 10, Issue 2, pp. 501 - 517
...), of the weights of the vertices. The Roman domination number is the minimum weight of a Roman dominating function in 𝐺... 
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
Discussiones Mathematicae. Graph Theory, ISSN 2083-5892, 2019, Volume 39, Issue 2, pp. 519 - 532
... ) ≤ ) ≤ 3 ), where ) is the domination number of , and they raised the problem of characterizing the graphs achieving these upper and lower bounds... 
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
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 11/2017, Volume 37, Issue 4, pp. 1039 - 1053
Journal Article
Journal Article
Discussiones Mathematicae. Graph Theory, ISSN 2083-5892, 2017, Volume 37, Issue 1, pp. 261 - 272
... is ) = ∑ ). The signed total Roman domination number ) of is the minimum weight of an STRDF on . In this paper we initiate the study of the signed total Roman domination number of digraphs, and we present different bounds... 
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, 2019, Volume 39, Issue 4, pp. 787 - 803
.... The minimum weight of a total Roman dominating function on a graph G is called the total Roman domination number of G... 
MATHEMATICS | total Roman reinforcement number | NUMBER | total Roman domination number | TOTAL DOMINATION | 05C69
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2019, Volume 263, pp. 257 - 270
.... The weight of f is w(f)=∑v∈V(G)f(v). The weak Roman domination number of a graph G, denoted by γr(G... 
Lexicographic product | Domination in graphs | Total domination | Weak roman domination | Double total domination | MATHEMATICS, APPLIED | Minimum weight | Graphs | Mathematical functions | Apexes | Invariants
Journal Article
Discussiones Mathematicae. Graph Theory, ISSN 1234-3099, 2017, Volume 37, Issue 4, pp. 1027 - 1038
... (of functions) on G. The maximum number of functions in a signed total Roman k-dominating family on G is the signed total Roman k-domatic number of G, denoted by d (G... 
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 Applied Mathematics, ISSN 0166-218X, 06/2019, Volume 263, pp. 88 - 95
.... The total Roman domination number of G is the minimum value of the sums ∑v∈Vf(v) over all total Roman dominating functions f of G... 
Roman domination | Total Roman domination | Lexicographic product graphs | MATHEMATICS, APPLIED | NUMBER | Graphs | Mathematical functions | Graph theory | Apexes
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 12/2014, Volume 178, pp. 27 - 32
.... We show that for all graphs, the weak Roman domination number is bounded above by the 2-rainbow domination number... 
Roman domination | Total domination | Weak Roman domination | 2-domination | Secure domination | 2-rainbow domination | MATHEMATICS, APPLIED | RAINBOW DOMINATION | GRAPHS
Journal Article
Ars combinatoria, ISSN 0381-7032, 04/2020, Volume 150, pp. 225 - 240
.... The weight of a total Roman dominating function f is the value Sigma(u is an element of V(G))f(u). The total Roman domination number of G... 
MATHEMATICS | total Roman domination number | total Roman dominating function
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 09/2020, Volume 284, pp. 290 - 300
.... The minimum cardinality among all double dominating sets of G is the double domination number... 
Double domination | Lexicographic product | Total Roman [formula omitted]-domination | Total domination | MATHEMATICS, APPLIED | NUMBER | TOTAL ROMAN DOMINATION | Total Roman {2}-domination | Mathematics - Combinatorics
Journal Article
Discrete mathematics, algorithms, and applications, ISSN 1793-8309, 04/2018, Volume 10, Issue 2
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2019, Volume 269, pp. 107 - 119
... ω(f)=∑w∈Vf(w) of any outer-independent total Roman dominating function on G is the outer-independent total Roman domination number, γoitR(G), of G... 
Vertex cover | Roman domination | Vertex independence | Total Roman domination | Total domination | Outer-independent total Roman domination | MATHEMATICS, APPLIED | Minimum weight | Graphs | Mathematical functions | Apexes | Combinatorial analysis
Journal Article
Journal Article
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