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Discrete Applied Mathematics, ISSN 0166-218X, 2016, Volume 204, pp. 22 - 28
...}-dominating function f is the Roman {2}-domination number. First, we present bounds relating the Roman {2... 
Roman domination | Weak Roman domination | 2-domination | Roman [formula omitted]-domination | 2-rainbow domination | Roman {2}-domination | Computer science | Functions (mathematics) | Minimum weight | Trees | Mathematical analysis | Graphs | Roman | Graph theory
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 09/2020, Volume 283, pp. 555 - 564
...}-dominating function on G is the Roman {3}-domination number of G, denoted by γ{R3}(G). We initiate the study of Roman {3... 
Roman [formula omitted]-domination | (Roman, Roman [formula omitted], double roman) domination | MATHEMATICS, APPLIED | Roman {3}-domination | (Roman, Roman {2}, double roman) domination | Minimum weight | Graphs | Mathematical functions | Upper bounds
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 12/2017, Volume 232, pp. 1 - 7
...). The double Roman domination number γdR(G) is the minimum weight of a DRDF on G. First we show that the decision problem associated with γdR(G... 
Roman [formula omitted]-domination | Double Roman domination | Roman domination | Roman {2}-domination | MATHEMATICS, APPLIED | NUMBER
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2017, Volume 217, pp. 557 - 564
The Roman domination number and Italian domination number (also known as the Roman {2}-domination number... 
Dominating set | Tree | Roman [formula omitted]-dominating set | Roman {2}-dominating set | MATHEMATICS, APPLIED | Roman -dominating set | ROMAN DOMINATION | GRAPHS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2018, Volume 236, pp. 408 - 414
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 10/2020, Volume 285, pp. 227 - 241
The Roman domination problem (RDP) aims to find an optimal strategy to defend a graph or network with the least number of defenders... 
Roman domination | Benders decomposition | [formula omitted]-strong roman domination | L-shaped method | k-strong roman domination | MATHEMATICS, APPLIED | ALGORITHMS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 05/2019, Volume 260, pp. 164 - 177
.... The perfect Italian domination number of G, denoted γIp(G), is the minimum weight of a perfect Italian dominating function of G... 
Roman [formula omitted]-domination | Roman domination | Italian domination | MATHEMATICS, APPLIED | Roman {2)-domination | Minimum weight | Mathematical functions | Trees (mathematics) | Apexes
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 09/2020, Volume 284, pp. 290 - 300
.... In this article, we obtain tight bounds and closed formulas for the double domination number of lexicographic product graphs G... 
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 Applied Mathematics, ISSN 0166-218X, 09/2020, Volume 284, pp. 384 - 390
Given a graph G, we consider γr(G), γ{R2}(G), γr2(G) and γR(G) as the weak Roman domination number, the Roman {2... 
Roman domination | Tree | Weak Roman domination | Roman [formula omitted]-domination | 2-rainbow domination | MATHEMATICS, APPLIED | Roman {2}-domination
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 05/2015, Volume 186, Issue 1, pp. 98 - 105
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2009, Volume 157, Issue 7, pp. 1634 - 1639
... . The k - domination number γ k ( G ) is the minimum cardinality among the k -dominating sets of G... 
Domination | [formula omitted]-domination | [formula omitted]-Roman domination | k-domination | k-Roman domination | MATHEMATICS, APPLIED | GRAPHS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 04/2019, Volume 258, pp. 235 - 241
A Roman{2}-dominating function of a graph G with vertex set V(G) is defined in Chellali et al. (2016) as a function f:V(G)→{0,1,2} having the property that if... 
Domination | Roman [formula omitted]-domination | Roman [formula omitted]-domatic number | Roman {2}-domatic number | Roman {2}-domination | MATHEMATICS, APPLIED | Graphs | Mathematical functions
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 01/2015, Volume 180, pp. 150 - 157
Let k≥1 be an integer. A signed Romank-dominating function on a graph G is a function f:V(G)⟶{−1,1,2} such that ∑u∈N[v]f(u)≥k for every v∈V(G), where N[v] is... 
Signed Roman [formula omitted]-domination number | Signed Roman [formula omitted]-dominating function | Signed Roman [formula omitted]-domatic number | Signed Roman k-dominating function | Signed Roman k-domatic number | Signed Roman k-domination number | MATHEMATICS, APPLIED
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 1/2016, Volume 32, Issue 1, pp. 79 - 92
...$$ G is the Roman domination number of $$G$$ G . In this paper, we define the Roman independence number, the upper Roman domination number and the upper and lower... 
Roman independence | Roman domination | Mathematics | Engineering Design | Combinatorics | Roman irredundance | Roman parameters | MATHEMATICS | Computer science | Minimum weight | Chains | Mathematical functions | Sharpness | Inequalities | Texts | Graphs | Roman | Combinatorial analysis
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 7/2015, Volume 31, Issue 4, pp. 813 - 825
... (RDF). The weight of an RDF is the sum of its function value over all vertices. The Roman domination number of $$G$$ G , denoted by $$\gamma _{R}(G)$$ γ R ( G... 
Global Roman dominating function | Global Roman domination number | Roman domination number | Mathematics | Engineering Design | Roman dominating function | Combinatorics | 05C69 | MATHEMATICS | Graphs | Mathematical functions
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 5/2016, Volume 32, Issue 3, pp. 1217 - 1227
... is $$w(f)=\sum _{v\in V(D)}f(v)$$ w ( f ) = ∑ v ∈ V ( D ) f ( v ) . The signed Roman k-domination number $$\gamma _{sR}^k(D)$$ γ s R k ( D... 
Signed Roman k -domination number | 05C20 | Mathematics | Engineering Design | Combinatorics | Digraph | Signed Roman k -dominating function | 05C69 | Signed Roman k-dominating function | Signed Roman k-domination number | Integers | Minimum weight | Mathematical analysis | Texts | Graphs | Roman | Graph theory | Combinatorial analysis
Journal Article
International Journal of Computer Mathematics, ISSN 0020-7160, 07/2016, Volume 93, Issue 7, pp. 1093 - 1102
... for which . The weight of a RDF f is the sum , and the minimum weight of a RDF for G is the Roman domination number, of G... 
Roman domination | maximal Roman domination | MATHEMATICS, APPLIED | Graphs | Mathematical functions | Minimum weight | Trees | Mathematical analysis | Images | Mathematical models | Roman
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 5/2013, Volume 29, Issue 3, pp. 527 - 533
...)}$$ . The Roman domination number, γ R (G), of G is the minimum weight of a Roman dominating function on G... 
Domination | Roman domination | Mathematics | Critical | Engineering Design | Combinatorics | MATHEMATICS | Graphs | Roman | Combinatorial analysis
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2019, Volume 257, pp. 1 - 11
.... The weight of an SDRDF f is ∑u∈V(G)f(u), the minimum weight of an SDRDF is the signed double Roman domination number γsdR(G) of G... 
Double Roman domination | Signed double Roman domination | Roman domination | MATHEMATICS, APPLIED | Minimum weight | Graphs | Mathematical functions | Trees (mathematics) | Apexes
Journal Article
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