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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
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
Discrete mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 1, pp. 32 - 63
... in S . In this paper, we offer a survey of selected recent results on total domination in graphs. 
Total domination number | Total domination | INTERVAL | NUMBER | PAIRED-DOMINATION | SIGNED TOTAL DOMINATION | MATHEMATICS | TREES | EQUAL TOTAL DOMINATION | PARALLEL ALGORITHMS | COMPLEXITY | PLANAR GRAPHS | TOTAL RESTRAINED DOMINATION
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 10/2016, Volume 32, Issue 3, pp. 855 - 871
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 1/2016, Volume 31, Issue 1, pp. 333 - 346
...$$ G , is called the signed Roman edge domination number of $$G$$ G and is denoted by $$\gamma _{sR}'(G)$$ γ s R ′ ( G ) . In this note we initiate the study of the signed Roman edge domination in graphs and present... 
Convex and Discrete Geometry | Signed Roman dominating function | Signed Roman edge domination number | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | 05C69 | Signed Roman domination number | Signed Roman edge dominating function | Optimization | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 5/2016, Volume 32, Issue 3, pp. 1217 - 1227
... is $$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)$$ γ s R k ( D... 
Signed Roman k -domination number | 05C20 | Mathematics | Engineering Design | Combinatorics | Digraph | Signed Roman k -dominating function | 05C69 | Signed Roman k-dominating function | Signed Roman k-domination number | Integers | Minimum weight | Mathematical analysis | Texts | Graphs | Roman | Graph theory | Combinatorial analysis
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 7/2016, Volume 32, Issue 1, pp. 299 - 317
Journal Article
Iranian Journal of Science and Technology, Transactions A: Science, ISSN 1028-6276, 6/2017, Volume 41, Issue 2, pp. 383 - 391
... ) , and two vertices $$x$$ x and $$y$$ y are adjacent if and only if $$x \ne y$$ x ≠ y and $$xy = yx$$ x y = y x . In this paper, we consider the domination and signed domination numbers on commuting graph... 
Engineering | Life Sciences, general | Commuting graph | Chemistry/Food Science, general | Non-commutative ring | Materials Science, general | Domination number | Earth Sciences, general | Signed domination number | Engineering, general | Physics, general | NUMBER | RINGS | MULTIDISCIPLINARY SCIENCES | Graph theory | Apexes | Upper bounds | Commuting | Mathematics - Rings and Algebras
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 11/2017, Volume 37, Issue 4, pp. 1039 - 1053
Journal Article
Discussiones Mathematicae. Graph Theory, ISSN 2083-5892, 2017, Volume 37, Issue 1, pp. 261 - 272
... is ) = ∑ ). The signed total Roman domination number ) of is the minimum weight of an STRDF on . In this paper we initiate the study of the signed total Roman domination number of digraphs, and we present different bounds... 
05C20 | signed total Roman dominating function | 05C69 | digraph | signed total Roman domination number | Digraph | Signed total Roman domination number | Signed total Roman dominating function | MATHEMATICS | GRAPHS
Journal Article
Discussiones Mathematicae. Graph Theory, ISSN 2083-5892, 2017, Volume 37, Issue 1, pp. 39 - 53
... for which ) = −1 is adjacent to at least one edge ′ for which ′) = 2. The minimum of the values ∑ ), taken over all signed Roman edge -dominating functions of is called the signed Roman edge -domination number of , and is denoted by γ... 
dominating function | domination number | 05C69 | signed Roman edge | Signed Roman edge k-dominating function | Signed Roman edge k-domination number | MATHEMATICS | signed Roman edge k-domination number | signed Roman edge k-dominating function
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 1/2016, Volume 32, Issue 1, pp. 175 - 190
... . The weight of an SRkDF $$f$$ f is $$w(f)=\sum _{v\in V(G)}f(v)$$ w ( f ) = ∑ v ∈ V ( G ) f ( v ) . The signed Roman $$k$$ k -domination number... 
Signed Roman k -domination number | Mathematics | Engineering Design | Combinatorics | Signed Roman k -dominating function | 05C69
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, 11/2017, Volume 37, Issue 4, pp. 989 - 1004
... (TMTDF) if f(N−(v)) ≥ 1 and f(N+(v)) ≥ 1 for each vertex v ∈ V. The twin minus total domination number of D is y*mt(D) = min{w(f) | f is a TMTDF of D... 
directed graph | twin minus total domination number | twin minus total dominating function | Twin minus total dominating function | Directed graph | Twin minus total domination number | MATHEMATICS | SIGNED TOTAL DOMINATION
Journal Article
Acta Mathematica Sinica, English Series, ISSN 1439-8516, 5/2018, Volume 34, Issue 5, pp. 911 - 920
Let G = (V, E) be a simple graph. A function f : E → {+1,−1} is called a signed cycle domination function (SCDF) of G if Ʃ e∈E(C) f(e... 
Domination number | Mathematics, general | Mathematics | planar graph | signed cycle domination function | maximal planar graph | 05C69 | signed cycle domination number | MATHEMATICS | MATHEMATICS, APPLIED | Graphs | Mathematical functions | Graph theory
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2019, Volume 39, Issue 1, pp. 67 - 79
...). The signed Roman k-domination number γ (D) of a digraph D is the minimum weight of an SRkDF on D... 
05C20 | signed Roman k-domination number | signed Roman k-dominating function | 05C69 | digraph | oriented tree | Signed Roman k-domination number | Signed Roman k-dominating function | Digraph | Oriented tree | MATHEMATICS
Journal Article
Electronic journal of graph theory and applications, ISSN 2338-2287, 2016, Volume 1, Issue 2, pp. 231 - 237
... $V(G)$ to the set $\{-1,1\}$ such that $\sum_{u\in N[v]}f(u)\ge 0$ for every vertex $v\in V(G)$. The nonnegative signed domination number... 
Nonnegative signed domination number | Nonnegative signed dominating function | nonnegative signed dominating function, nonnegative signed domination number
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2016, Volume 36, Issue 2, pp. 467 - 477
In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter... 
tuple total domination number | open packing | signed total domination number | total limited packing | Signed total domination number | Total limited packing | Tuple total domination number | Open packing | MATHEMATICS | Mathematics - Combinatorics
Journal Article
Discrete mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 4, pp. 1007 - 1012
... ) ≥ 1 holds for any induced cycle C of G . The signed cycle domination number of G is defined as γ s c ′ ( G ) = min { ∑ e ∈ E ( G ) f ( e ) ∣ f is an SCDF of G... 
Signed cycle dominating function | Signed cycle domination number | Planar graph | MATHEMATICS | NUMBERS
Journal Article
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