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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
SIAM journal on discrete mathematics, ISSN 1095-7146, 2009, Volume 23, Issue 3, pp. 1575 - 1586
.... The Roman domination number gamma(R)(G) of G is the minimum of Sigma(v is an element of V... 
Domination | Roman domination number | Nordhaus-Gaddum inequality | GRAPH | MATHEMATICS, APPLIED | domination | EMPIRE | Lower bounds | Graphs | Labels | Roman | Marking | Mathematical analysis
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 2/2014, Volume 27, Issue 2, pp. 241 - 255
.... The signed Roman domination number of G is the minimum weight of a SRDF in G. We present various lower and upper bounds on the signed Roman domination number of a graph... 
Convex and Discrete Geometry | Operations Research/Decision Theory | Signed domination | Roman domination | Signed Roman domination | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Combinatorics | Optimization | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
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 1234-3099, 11/2017, Volume 37, Issue 4, pp. 953 - 961
For a graph G, let R(G) and y (G) denote the Roman domination number of G and the 2-rainbow domination number of G, respectively... 
Roman domination | 2-rainbow domination | MATHEMATICS | GRAPHS
Journal Article
Journal of combinatorial optimization, ISSN 1573-2886, 2017, Volume 35, Issue 1, pp. 126 - 133
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 9/2019, Volume 42, Issue 5, pp. 1907 - 1920
... ) . The double Roman domination number of a digraph D is the minimum weight of a DRDF on D. In this paper, we initiate the study of the double Roman domination of digraphs... 
05C20 | Nordhaus–Gaddum | Signed domination | Double Roman domination | Mathematics, general | Roman domination | Mathematics | Applications of Mathematics | Digraph | 05C69 | k -domination | k-domination | MATHEMATICS | NUMBERS | Nordhaus-Gaddum | Minimum weight | Mathematical functions | Graph theory
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 10/2015, Volume 30, Issue 3, pp. 456 - 467
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 10/2017, Volume 40, Issue 4, pp. 1443 - 1454
... is $$\omega (f)=\sum _{x\in V\cup E}f(x)$$ ω(f)=∑x∈V∪Ef(x) . The mixed Roman domination number of G is the minimum weight of a mixed Roman dominating function of G... 
Roman domination number | Mixed Roman dominating function | Mathematics, general | Mathematics | Applications of Mathematics | Roman dominating function | 05C69 | Mixed Roman domination number | MATHEMATICS | NUMBERS | Minimum weight | Graphs | Mathematical functions
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$$ G . In this paper, we define the Roman independence number, the upper Roman domination number and the upper and lower... 
Roman independence | Roman domination | Mathematics | Engineering Design | Combinatorics | Roman irredundance | Roman parameters | MATHEMATICS | Computer science | Minimum weight | Chains | Mathematical functions | Sharpness | Inequalities | Texts | Graphs | Roman | Combinatorial analysis
Journal Article
Iranian Journal of Science and Technology, Transactions A: Science, ISSN 1028-6276, 6/2019, Volume 43, Issue 3, pp. 1081 - 1088
.... The double Roman domination number $$\gamma _{\rm dR}(G)$$ γ dR ( G ) equals the minimum weight of a double Roman dominating function on G... 
Domination | Trees | Engineering | Life Sciences, general | Chemistry/Food Science, general | Materials Science, general | Double Roman domination | Roman domination | Earth Sciences, general | Engineering, general | Physics, general | 05C69 | MULTIDISCIPLINARY SCIENCES
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 7/2015, Volume 31, Issue 4, pp. 813 - 825
... (RDF). The weight of an RDF is the sum of its function value over all vertices. The Roman domination number of $$G$$ G , denoted by $$\gamma _{R}(G)$$ γ R ( G... 
Global Roman dominating function | Global Roman domination number | Roman domination number | Mathematics | Engineering Design | Roman dominating function | Combinatorics | 05C69 | MATHEMATICS | Graphs | Mathematical functions
Journal Article
Journal of combinatorial optimization, ISSN 1573-2886, 2012, Volume 26, Issue 3, pp. 608 - 619
Journal Article
Resultate der Mathematik, ISSN 1420-9012, 2019, Volume 74, Issue 4, pp. 1 - 18
...) . The minimum weight of a quasi-total Roman dominating function on a graph G is called the quasi-total Roman domination number of G... 
Mathematics, general | Mathematics | Quasi-total Roman domination number | Roman domination number | total Roman domination number | 05C69 | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 9/2016, Volume 32, Issue 5, pp. 1731 - 1747
... with $$f(e)=0$$ f ( e ) = 0 is adjacent to some edge $$e'$$ e ′ with $$f(e')=2$$ f ( e ′ ) = 2 . The edge Roman domination number of G, denoted... 
K_{2, 3}$$ K 2 , 3 -subdivision-free graph | Edge Roman domination | Planar graph | Subcubic graph | Mathematics | Engineering Design | Combinatorics | k -degenerate graph | subdivision-free graph | K | k-degenerate graph | MATHEMATICS | K-2,K-3-subdivision-free graph
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
Discrete Applied Mathematics, ISSN 0166-218X, 10/2016, Volume 211, pp. 23 - 29
...), and the minimum weight of a double Roman dominating function on G is the double Roman domination number of G... 
Domination | Double Roman domination | Roman domination | MATHEMATICS, APPLIED | EMPIRE | STRATEGY | GRAPHS
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2019, Volume 39, Issue 2, pp. 455 - 472
... on . In this paper, we give a characterization of graphs of order for which co-Roman domination number... 
co-Roman domination number | co-Roman dominating function | Roman domination | 05C69 | MATHEMATICS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 19, pp. 5820 - 5827
... − X is adjacent to a vertex v ∈ X such that ( X − { v } ) ∪ { u } is dominating. The minimum cardinality of such a set is called the secure domination number, denoted by γ s ( G... 
ER-critical graph | Protection of a graph | Edge-removal-critical graph | Secure domination | MATHEMATICS | ROMAN-EMPIRE | TREES | PROTECTION
Journal Article
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