Graphs and combinatorics, ISSN 1435-5914, 2011, 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

Discrete mathematics, ISSN 0012-365X, 11/2015, Volume 338, Issue 11, pp. 2095 - 2104

We consider two general frameworks for multiple domination, which are called 〈r,s〉-domination and parametric domination. They generalise and unify...

Threshold functions | Total [formula omitted]-domination | Upper bounds | [formula omitted]-domination | Parametric domination | [formula omitted]-tuple domination | k-domination | k-tuple domination | { k } -domination | (r, s) -domination | Total k-domination | MATHEMATICS | NUMBER | < r, s >-domination | BOUNDS | k}-domination | GRAPHS

Threshold functions | Total [formula omitted]-domination | Upper bounds | [formula omitted]-domination | Parametric domination | [formula omitted]-tuple domination | k-domination | k-tuple domination | { k } -domination | (r, s) -domination | Total k-domination | MATHEMATICS | NUMBER | < r, s >-domination | BOUNDS | k}-domination | GRAPHS

Journal Article

Theoretical computer science, ISSN 0304-3975, 11/2019, Volume 795, pp. 128 - 141

Given a positive integer k, a k-dominating set in a graph G is a set of vertices such that every vertex not in the set has at least k neighbors in the set. A...

k-domination | Polynomial-time algorithm | Proper interval graph | Total k-domination | COMPLEXITY | SETS | EFFICIENT ALGORITHMS | TUPLE TOTAL DOMINATION | COMPUTER SCIENCE, THEORY & METHODS

k-domination | Polynomial-time algorithm | Proper interval graph | Total k-domination | COMPLEXITY | SETS | EFFICIENT ALGORITHMS | TUPLE TOTAL DOMINATION | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2020, Volume 40, Issue 1, pp. 209 - 225

In this paper we introduce and study a new graph invariant derived from the degree sequence of a graph
, called the
and denoted sub
). This invariant serves as...

Slater number | sub | domination number | degree sequence index strategy | 05C69 | MATHEMATICS | BOUNDS | sub-k-domination number | k-domination number | slater number | 05c69

Slater number | sub | domination number | degree sequence index strategy | 05C69 | MATHEMATICS | BOUNDS | sub-k-domination number | k-domination number | slater number | 05c69

Journal Article

Journal of Combinatorial Optimization, ISSN 1382-6905, 2/2014, Volume 27, Issue 2, pp. 292 - 301

Let k be a positive integer and G=(V,E) be a graph. A vertex subset D of a graph G is called a perfect k-dominating set of G, if every vertex v of G, not in D,...

Perfect k -domination | NP-Completeness | Convex and Discrete Geometry | Operations Research/Decision Theory | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Dynamic programming | Combinatorics | k -Domination | Optimization | k-Domination | Perfect k-domination | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Algorithms

Perfect k -domination | NP-Completeness | Convex and Discrete Geometry | Operations Research/Decision Theory | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Dynamic programming | Combinatorics | k -Domination | Optimization | k-Domination | Perfect k-domination | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Algorithms

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2018, Volume 38, Issue 1, pp. 301 - 317

Let
= (
) be a graph; a set
⊆
is a total
-dominating set if every vertex
∈
has at least
neighbors in
. The total
-domination number
) is the minimum...

total | domination | 05C69 | tuple total domination | tuple domination | K-tuple total domination | K-tuple domination | K-domination | Total k-domination | k-domination | MATHEMATICS | k-tuple total domination | total k-domination | k-tuple domination

total | domination | 05C69 | tuple total domination | tuple domination | K-tuple total domination | K-tuple domination | K-domination | Total k-domination | k-domination | MATHEMATICS | k-tuple total domination | total k-domination | k-tuple domination

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 9/2019, Volume 42, Issue 5, pp. 1907 - 1920

Let D be a finite and simple digraph with vertex set V(D). A double Roman dominating function (DRDF) on a digraph D is a function
$$f:V(D)\rightarrow...

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

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 Applied Mathematics and Computing, ISSN 1598-5865, 2/2018, Volume 56, Issue 1, pp. 73 - 91

Zhang introduced the concept of bipolar fuzzy sets as a generalization of fuzzy sets. Bipolar fuzzy sets have shown advantages in solving decision making...

03E72 | Computational Mathematics and Numerical Analysis | Mathematics of Computing | 68R05 | Mathematical and Computational Engineering | Restrained domination (RD) and global restrained domination (GRD) | Equitable domination (ED) | Mathematics | Theory of Computation | Decision making problem | 68R10 | k -domination | k-domination | MATHEMATICS | MATHEMATICS, APPLIED | DOMINATION | Decision-making | Algorithms | Scientific papers | Fuzzy sets | Graphs | Decision making

03E72 | Computational Mathematics and Numerical Analysis | Mathematics of Computing | 68R05 | Mathematical and Computational Engineering | Restrained domination (RD) and global restrained domination (GRD) | Equitable domination (ED) | Mathematics | Theory of Computation | Decision making problem | 68R10 | k -domination | k-domination | MATHEMATICS | MATHEMATICS, APPLIED | DOMINATION | Decision-making | Algorithms | Scientific papers | Fuzzy sets | Graphs | Decision making

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 17

Let
G
=
(
V
(
G
)
,
E
(
G
)
)
$G=(V(G),E(G))$
be a graph. A set
D
⊆
V
(
G
)
$D\subseteq V(G)$
is a distance k-dominating set of G if for every vertex
u
∈
V
(
G...

first Zagreb index | distance k -domination number | Analysis | Mathematics, general | second Zagreb index | Mathematics | Applications of Mathematics | 05C69 | 05C35 | trees | distance k-domination number | MATHEMATICS, APPLIED | ENERGY | SHARP BOUNDS | SUM | TOPOLOGICAL DESCRIPTOR | MATHEMATICS | UPPER-BOUNDS | MOLECULAR-ORBITALS | WIENER INDEX | COVERING NUMBERS | UNICYCLIC GRAPHS | BIPARTITE GRAPHS | Research

first Zagreb index | distance k -domination number | Analysis | Mathematics, general | second Zagreb index | Mathematics | Applications of Mathematics | 05C69 | 05C35 | trees | distance k-domination number | MATHEMATICS, APPLIED | ENERGY | SHARP BOUNDS | SUM | TOPOLOGICAL DESCRIPTOR | MATHEMATICS | UPPER-BOUNDS | MOLECULAR-ORBITALS | WIENER INDEX | COVERING NUMBERS | UNICYCLIC GRAPHS | BIPARTITE GRAPHS | Research

Journal Article

Journal of Combinatorial Mathematics and Combinatorial Computing, ISSN 0835-3026, 2016, Volume 98, pp. 343 - 349

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 5/2016, Volume 32, Issue 3, pp. 1217 - 1227

Let
$$k\ge 1$$
k
≥
1
be an integer, and let D be a finite and simple digraph with vertex set V(D). A signed Roman k-dominating function (SRkDF) on a digraph 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

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

Computers & operations research, ISSN 0305-0548, 2018, Volume 96, pp. 69 - 79

•New approach to place charging stations for electric vehicles in road networks.•Computing reachability graphs for road networks and finding multiple...

Electric vehicles | k-Domination | Road networks | Facility location problem | Heuristic optimization | α-Domination | DESIGN | alpha-Domination | GRAPHS | UPPER-BOUNDS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INFRASTRUCTURE | ENGINEERING, INDUSTRIAL

Electric vehicles | k-Domination | Road networks | Facility location problem | Heuristic optimization | α-Domination | DESIGN | alpha-Domination | GRAPHS | UPPER-BOUNDS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INFRASTRUCTURE | ENGINEERING, INDUSTRIAL

Journal Article

Journal of Combinatorial Optimization, ISSN 1382-6905, 2/2017, Volume 33, Issue 2, pp. 365 - 372

The complementary prism
$$G\bar{G}$$
G
G
¯
of a graph G arises from the disjoint union of the graph G and its complement
$$\bar{G}$$
G
¯
by adding the edges of...

P_3$$ P 3 -Convexity | Convex and Discrete Geometry | Complementary prism | Clique | Independent set | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | k -Domination | Optimization | k-Domination | Convexity | P-3-Convexity | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DOMINATION | Hardness | Analysis

P_3$$ P 3 -Convexity | Convex and Discrete Geometry | Complementary prism | Clique | Independent set | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | k -Domination | Optimization | k-Domination | Convexity | P-3-Convexity | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DOMINATION | Hardness | Analysis

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2019, Volume 39, Issue 1, pp. 67 - 79

Let k be a positive integer. A signed Roman k-dominating function (SRkDF) on a digraph D is a function f : V (D) → {−1, 1, 2} satisfying the conditions that...

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

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

Aequationes mathematicae, ISSN 0001-9054, 4/2016, Volume 90, Issue 2, pp. 271 - 279

Let G be a graph with vertex set V(G). For any integer k ≥ 1, a signed total k-dominating function is a function f: V(G) → {−1, 1} satisfying ∑
x∈N(v)
f(x) ≥ k...

Mathematics | Combinatorics | 05C69 | Signed total k -dominating function | signed total k -domination number | Analysis | Signed total k-dominating function | signed total k-domination number | MATHEMATICS | MATHEMATICS, APPLIED | Lower bounds | Mathematical functions | Functions (mathematics) | Integers | Graphs | Mathematical analysis

Mathematics | Combinatorics | 05C69 | Signed total k -dominating function | signed total k -domination number | Analysis | Signed total k-dominating function | signed total k-domination number | MATHEMATICS | MATHEMATICS, APPLIED | Lower bounds | Mathematical functions | Functions (mathematics) | Integers | Graphs | Mathematical analysis

Journal Article

AKCE International Journal of Graphs and Combinatorics, ISSN 0972-8600, 04/2016, Volume 13, Issue 1, pp. 31 - 37

Efficiency and reliability are two important criteria in the designing of a good interconnection network. Network topological notions such as wide diameter,...

Wide diameter | Diameter vulnerability | [formula omitted]-domination | Fault diameter | Mycielskian | domination | (l, k)-domination | (l,k)-domination

Wide diameter | Diameter vulnerability | [formula omitted]-domination | Fault diameter | Mycielskian | domination | (l, k)-domination | (l,k)-domination

Journal Article

Filomat, ISSN 0354-5180, 2017, Volume 31, Issue 12, pp. 3925 - 3944

We prove the following result: If G be a connected graph on n >= 6 vertices, then there exists a set of vertices D with vertical bar D vertical bar <= n/3 and...

Domination | Independent set | Isolation | CONNECTED DOMINATION | MATHEMATICS | MATHEMATICS, APPLIED | domination | K-DOMINATION | BOUNDS | SETS | isolation | independent set

Domination | Independent set | Isolation | CONNECTED DOMINATION | MATHEMATICS | MATHEMATICS, APPLIED | domination | K-DOMINATION | BOUNDS | SETS | isolation | independent set

Journal Article

Journal of the Korean Mathematical Society, ISSN 0304-9914, 2009, Volume 46, Issue 6, pp. 1309 - 1318

Let k be a positive integer, and let G be a simple graph with vertex set V(G). A Roman k-dominating function on G is a function f : V(G) -> {0, 1, 2} such that...

Domination | Roman domination | Kdomination | Roman k-domination | k-domination | MATHEMATICS | MATHEMATICS, APPLIED | domination

Domination | Roman domination | Kdomination | Roman k-domination | k-domination | MATHEMATICS | MATHEMATICS, APPLIED | domination

Journal Article

Discrete mathematics, ISSN 0012-365X, 2017, Volume 340, Issue 3, pp. 494 - 503

As a natural variant of domination in graphs, Dankelmann et al. (2009) introduce exponential domination, where vertices are considered to have some dominating...

Domination | Exponential domination | MATHEMATICS | K-DOMINATION | DISTANCE DOMINATION | BROADCASTS | Computer Science | Discrete Mathematics

Domination | Exponential domination | MATHEMATICS | K-DOMINATION | DISTANCE DOMINATION | BROADCASTS | Computer Science | Discrete Mathematics

Journal Article

Theoretical computer science, ISSN 0304-3975, 08/2017, Volume 689, pp. 27 - 35

We consider an iterative irreversible process on graphs. Starting with some initial set S of vertices of a given graph G, this process iteratively adds to S...

Target set | Dynamic monopoly | Irreversible threshold processes | IRREVERSIBLE CONVERSION | DYNAMIC MONOPOLIES | K-DOMINATION NUMBER | APPROXIMABILITY | PERCOLATION | COMPUTER SCIENCE, THEORY & METHODS | Hardness | Management science | Algorithms

Target set | Dynamic monopoly | Irreversible threshold processes | IRREVERSIBLE CONVERSION | DYNAMIC MONOPOLIES | K-DOMINATION NUMBER | APPROXIMABILITY | PERCOLATION | COMPUTER SCIENCE, THEORY & METHODS | Hardness | Management science | Algorithms

Journal Article

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