Graphs and Combinatorics, ISSN 0911-0119, 1/2012, Volume 28, Issue 1, pp. 1 - 55

In 1985, Fink and Jacobson gave a generalization of the concepts of domination and independence in graphs. For a positive integer k, a subset S of vertices in...

k -Tuple domination | l -Total k -domination | Connected k -domination | k -Independence | k -Irredundance | Mathematics | k -Star-forming | Engineering Design | Combinatorics | k -Domination | 05C69 | l-Total k-domination | k-Domination | k-Star-forming | k-Irredundance | Connected k-domination | k-Independence | k-Tuple domination | P-DOMINATION | F-DOMINATION | IRREDUNDANCE | EQUAL DOMINATION | TRANSVERSAL NUMBERS | CONJECTURE | MATHEMATICS | TREES | BOUNDS | 2-DOMINATION NUMBER | TUPLE DOMINATION | Graphs | Star & galaxy formation | Integers | Combinatorial analysis

k -Tuple domination | l -Total k -domination | Connected k -domination | k -Independence | k -Irredundance | Mathematics | k -Star-forming | Engineering Design | Combinatorics | k -Domination | 05C69 | l-Total k-domination | k-Domination | k-Star-forming | k-Irredundance | Connected k-domination | k-Independence | k-Tuple domination | P-DOMINATION | F-DOMINATION | IRREDUNDANCE | EQUAL DOMINATION | TRANSVERSAL NUMBERS | CONJECTURE | MATHEMATICS | TREES | BOUNDS | 2-DOMINATION NUMBER | TUPLE DOMINATION | Graphs | Star & galaxy formation | Integers | Combinatorial analysis

Journal Article

Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 4/2019, Volume 13, Issue 1, pp. 261 - 289

In this paper we introduce a domination game based on the notion of connected domination. Let = ( ) be a connected graph of order at least 2. We define a on as...

Leaves | Optimal strategies | Cardinality | Games | Discrete mathematics | Graph theory | Mathematics | Cartesianism | Vertices | Induction assumption | MATHEMATICS | MATHEMATICS, APPLIED | Connected domination | 3/5-CONJECTURE | EXTREMAL FAMILIES | 2-tree | connected domination game | domination games on graphs | Cartesian product | GRAPHS

Leaves | Optimal strategies | Cardinality | Games | Discrete mathematics | Graph theory | Mathematics | Cartesianism | Vertices | Induction assumption | MATHEMATICS | MATHEMATICS, APPLIED | Connected domination | 3/5-CONJECTURE | EXTREMAL FAMILIES | 2-tree | connected domination game | domination games on graphs | Cartesian product | GRAPHS

Journal Article

Iranian Journal of Science and Technology, Transactions A: Science, ISSN 1028-6276, 8/2019, Volume 43, Issue 4, pp. 1713 - 1718

Let $$G=(V,E)$$ G = ( V , E ) be a graph. For some $$\alpha$$ α with $$0<\alpha \le 1$$ 0 < α ≤ 1 , a subset S of V is said to be a $$\alpha$$ α -partial...

Engineering | Life Sciences, general | Chemistry/Food Science, general | Materials Science, general | Edge-critical graphs | Connected graph | Earth Sciences, general | alpha$$ α -Domination | Engineering, general | Physics, general | 05C69 | MULTIDISCIPLINARY SCIENCES | alpha-Domination | Mathematics - Combinatorics

Engineering | Life Sciences, general | Chemistry/Food Science, general | Materials Science, general | Edge-critical graphs | Connected graph | Earth Sciences, general | alpha$$ α -Domination | Engineering, general | Physics, general | 05C69 | MULTIDISCIPLINARY SCIENCES | alpha-Domination | Mathematics - Combinatorics

Journal Article

ACM Transactions on Algorithms (TALG), ISSN 1549-6325, 05/2019, Volume 15, Issue 2, pp. 1 - 90

We algorithmize the structural characterization for claw-free graphs by Chudnovsky and Seymour. Building on this result, we show that D ominating S et on...

fixed-parameter tractable | polynomial kernel | Claw-free graphs | dominating set | connected dominating set | MATHEMATICS, APPLIED | SET | PARTITION REFINEMENT | COMPLEXITY | COMPUTER SCIENCE, THEORY & METHODS | ALGORITHMS

fixed-parameter tractable | polynomial kernel | Claw-free graphs | dominating set | connected dominating set | MATHEMATICS, APPLIED | SET | PARTITION REFINEMENT | COMPLEXITY | COMPUTER SCIENCE, THEORY & METHODS | ALGORITHMS

Journal Article

Journal of Combinatorial Optimization, ISSN 1382-6905, 2019, Volume 38, Issue 1, pp. 292 - 315

The study of power domination in graphs arises from the problem of placing a minimum number of measurement devices in an electrical network while monitoring...

Power domination | Cactus graph | Connected power domination | NP-complete | Integer program | Zero forcing | Electric power systems | Electric properties

Power domination | Cactus graph | Connected power domination | NP-complete | Integer program | Zero forcing | Electric power systems | Electric properties

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 08/2019, Volume 267, pp. 151 - 159

A Roman dominating function on a graph G=(V,E) is defined to be a function f:V→{0,1,2} satisfying the condition that every vertex u for which f(u)=0 is...

Trees | Roman domination number | Weakly connected Roman domination number | Weakly connected set | MATHEMATICS, APPLIED | Minimum weight | Mathematical functions

Trees | Roman domination number | Weakly connected Roman domination number | Weakly connected set | MATHEMATICS, APPLIED | Minimum weight | Mathematical functions

Journal Article

Discrete Mathematics, ISSN 0012-365X, 09/2012, Volume 312, Issue 17, pp. 2672 - 2675

A k-dominating set in a graph G is a set S of vertices such that every vertex of G is at distance at most k from some vertex of S. Given a class D of finite...

Forbidden induced subgraph | Class of connected graphs | Dominating set | Distance domination | MATHEMATICS | SUBGRAPHS | GRAPHS | Constrictions | Chains | Graphs | Iterative methods | Mathematical analysis

Forbidden induced subgraph | Class of connected graphs | Dominating set | Distance domination | MATHEMATICS | SUBGRAPHS | GRAPHS | Constrictions | Chains | Graphs | Iterative methods | Mathematical analysis

Journal Article

Journal of Discrete Mathematical Sciences and Cryptography, ISSN 0972-0529, 07/2019, Volume 22, Issue 5, pp. 753 - 760

Let G = (V, E) be a undirected, finite, simple graph. A subset D of V is said to be dominating set if for every v in V - D there exists u in D such that u and...

Connected domination | 05C69 | Chromatic connected domination | Chromatic connected domination number

Connected domination | 05C69 | Chromatic connected domination | Chromatic connected domination number

Journal Article

Proceedings - Mathematical Sciences, ISSN 0253-4142, 2/2016, Volume 126, Issue 1, pp. 11 - 20

We initiate the study of outer-2-independent domination in graphs. An outer-2-independent dominating set of a graph G is a set D of vertices of G such that...

outer-connected domination | domination | cartesian product of graphs | Outer-2-independent domination | Mathematics, general | Mathematics | Vizing’s conjecture | 05C69 | Domination | Vizing's conjecture | Cartesian product of graphs | Outer-connected domination | MATHEMATICS | Mathematical research | Graphic methods | Research

outer-connected domination | domination | cartesian product of graphs | Outer-2-independent domination | Mathematics, general | Mathematics | Vizing’s conjecture | 05C69 | Domination | Vizing's conjecture | Cartesian product of graphs | Outer-connected domination | MATHEMATICS | Mathematical research | Graphic methods | Research

Journal Article

International Journal of Pure and Applied Mathematics, ISSN 1311-8080, 2015, Volume 105, Issue 4, pp. 751 - 761

Journal Article

Fasciculi Mathematici, ISSN 0044-4413, 06/2018, Volume 60, Issue 1, pp. 103 - 121

Let be a simple graph of order . The connected domination polynomial of is the polynomial , where ) is the number of connected dominating sets of of size and )...

Petersen graphs | graphs | 05C69 | connected domination polynomial | connected dominating set

Petersen graphs | graphs | 05C69 | connected domination polynomial | connected dominating set

Journal Article

Algebra and Discrete Mathematics, ISSN 1726-3255, 2017, Volume 24, Issue 2, pp. 320 - 330

Journal Article

Journal of Analysis and Applications, ISSN 0972-5954, 03/2016, Volume 14, Issue 1, pp. 1 - 19

Journal Article

Ars Combinatoria, ISSN 0381-7032, 01/2018, Volume 136, pp. 127 - 151

A graph G is said to be k-gamma(c)-critical if the connected domination number gamma(c)(G) of G is k and gamma(c)(G + uv) < k for every uv (sic) E(G). The...

Hamiltonian | Connected domination | Critical | MATHEMATICS | critical | 3-DOMINATION-CRITICAL GRAPHS | connected domination

Hamiltonian | Connected domination | Critical | MATHEMATICS | critical | 3-DOMINATION-CRITICAL GRAPHS | connected domination

Journal Article

Analele Universitatii "Ovidius" Constanta - Seria Matematica, ISSN 1224-1784, 06/2015, Volume 23, Issue 2, pp. 187 - 199

Let G = (V;E) be a graph. A set S ⊂ V (G) is a hop dominating set of G if for every v ∈ V - S, there exists u ∈ S such that d(u; v) = 2. The minimum...

Hop domination number | connected domination number | total domination number | Total domination number | Connected domination number | MATHEMATICS | MATHEMATICS, APPLIED

Hop domination number | connected domination number | total domination number | Total domination number | Connected domination number | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

International Journal of Applied Engineering Research, ISSN 0973-4562, 2019, Volume 14, Issue 7, pp. 1566 - 1569

Journal Article

Applied Mathematical Sciences, ISSN 1312-885X, 2015, Volume 9, Issue 13-16, pp. 665 - 668

Journal Article

Italian Journal of Pure and Applied Mathematics, ISSN 1126-8042, 07/2018, Issue 40, pp. 188 - 199

Journal Article

SYMMETRY-BASEL, ISSN 2073-8994, 09/2019, Volume 11, Issue 9, p. 1165

A total dominating set D of a graph G is said to be a secure total dominating set if for every vertex u is an element of V(G) \ D, there exists a vertex v is...

secure domination | independence number | domination | secure total domination | PROTECTION | ROMAN | MULTIDISCIPLINARY SCIENCES | matching number | OUTER-CONNECTED DOMINATION

secure domination | independence number | domination | secure total domination | PROTECTION | ROMAN | MULTIDISCIPLINARY SCIENCES | matching number | OUTER-CONNECTED DOMINATION

Journal Article

Journal of Combinatorial Mathematics and Combinatorial Computing, ISSN 0835-3026, 11/2014, Volume 91, pp. 31 - 50

Journal Article

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