Graphs and combinatorics, ISSN 1435-5914, 2011, Volume 28, Issue 1, pp. 1 - 55

...Graphs and Combinatorics (2012) 28:1–55
DOI 10.1007/s00373-011-1040-3
SURVEY
k-Domination and k-Independence in Graphs: A Survey
Mustapha Chellali · Odile...

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, algorithms, and applications, ISSN 1793-8309, 08/2017, Volume 9, Issue 4

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 1/2012, Volume 28, Issue 1, pp. 97 - 107

...Graphs and Combinatorics (2012) 28:97–107
DOI 10.1007/s00373-010-1012-z
ORIGINAL PAPER
Dominator Colorings in Some Classes of Graphs
Mustapha Chellali...

Coloring | Domination | Characterization | Dominator coloring | Mathematics | Engineering Design | Combinatorics | 05C69 | 05C15 | MATHEMATICS | Graphs | Combinatorial analysis | Color | Computer Science | Discrete Mathematics

Coloring | Domination | Characterization | Dominator coloring | Mathematics | Engineering Design | Combinatorics | 05C69 | 05C15 | MATHEMATICS | Graphs | Combinatorial analysis | Color | Computer Science | Discrete Mathematics

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 4/2016, Volume 90, Issue 2, pp. 355 - 366

... Mathematicae
Vertex-edge domination in graphs
Razika Boutrig, Mustapha Chellali, Teresa W. Haynes
and Stephen T. Hedetniemi
Abstract. In this paper we study graph...

domination | Analysis | tree | Mathematics | Vertex-edge domination | Combinatorics | 05C69 | MATHEMATICS | MATHEMATICS, APPLIED | Resveratrol | Graphs | Trees (mathematics) | Graph theory | Parameters | Upper bounds | Trees | Mathematical analysis

domination | Analysis | tree | Mathematics | Vertex-edge domination | Combinatorics | 05C69 | MATHEMATICS | MATHEMATICS, APPLIED | Resveratrol | Graphs | Trees (mathematics) | Graph theory | Parameters | Upper bounds | Trees | Mathematical analysis

Journal Article

Discrete mathematics, ISSN 0012-365X, 02/2017, Volume 340, Issue 2, pp. 31 - 38

Let G=(V,E) be a graph with vertex set V and edge set E. A vertex v∈Vve-dominates every edge incident to it as well as every edge adjacent to these incident...

Vertex | Edge–vertex domination | Vertex–edge degree | Degree | Edge–vertex degree | Irregular graph | Regular graph | Vertex–edge domination | MATHEMATICS | Vertex-edge degree | Edge-vertex degree | MOLECULAR-ORBITALS | Edge-vertex domination | Vertex-edge domination

Vertex | Edge–vertex domination | Vertex–edge degree | Degree | Edge–vertex degree | Irregular graph | Regular graph | Vertex–edge domination | MATHEMATICS | Vertex-edge degree | Edge-vertex degree | MOLECULAR-ORBITALS | Edge-vertex domination | Vertex-edge domination

Journal Article

Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica, ISSN 1232-9274, 2012, Volume 32, Issue 4, pp. 715 - 718

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

Independent Roman domination | Roman domination | Strong equality | strong equality | independent Roman domination

Independent Roman domination | Roman domination | Strong equality | strong equality | independent Roman domination

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 5/2015, Volume 31, Issue 3, pp. 713 - 727

... Haddad ·
Mustapha Chellali · Hamamache Kheddouci
Received: 13 June 2012 / Revised: 27 November 2013 / Published online: 16 March 2014
© Springer Japan 2014
Abstract...

Split graphs | Star-free graphs | Total domination | Algorithms | Triangle-free graphs | Dominated coloring | 05C85 | Mathematics | Engineering Design | Combinatorics | 05C15 | MATHEMATICS | TREES | Studies | Graphs | Color | Coloring | Equivalence | Texts | Polynomials | Recognition | Combinatorial analysis | Data Structures and Algorithms | Computer Science | Discrete Mathematics | Computational Complexity

Split graphs | Star-free graphs | Total domination | Algorithms | Triangle-free graphs | Dominated coloring | 05C85 | Mathematics | Engineering Design | Combinatorics | 05C15 | MATHEMATICS | TREES | Studies | Graphs | Color | Coloring | Equivalence | Texts | Polynomials | Recognition | Combinatorial analysis | Data Structures and Algorithms | Computer Science | Discrete Mathematics | Computational Complexity

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 10/2018, Volume 247, p. 294

A partition π={V1,V2,…,Vk} of the vertex set V of a graph G into k color classes Vi, with i∈{1,…,k}, is called a quorum coloring if, for every vertex v∈V, at...

Coloring | Theorems | Graph coloring | Color | Graph theory

Coloring | Theorems | Graph coloring | Color | Graph theory

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 2013, Volume 161, Issue 18, pp. 2885 - 2893

A subset S⊆V in a graph G=(V,E) is a [j,k]-set if, for every vertex v∈V∖S, j≤|N(v)∩S|≤k for non-negative integers j and k, that is, every vertex v∈V∖S is...

Domination | Grid graphs | [1, 2]-sets | Restrained domination | MATHEMATICS, APPLIED | CODES | SETS | [1,2]-sets | Integers | Mathematical analysis | Graphs

Domination | Grid graphs | [1, 2]-sets | Restrained domination | MATHEMATICS, APPLIED | CODES | SETS | [1,2]-sets | Integers | Mathematical analysis | Graphs

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 1/2016, Volume 32, Issue 1, pp. 79 - 92

...Graphs and Combinatorics (2016) 32:79–92
DOI 10.1007/s00373-015-1566-x
ORIGINAL PAPER
A Roman Domination Chain
Mustapha Chellali 1 · Teresa W. Haynes 2 , 3...

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

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

Discrete Applied Mathematics, ISSN 0166-218X, 02/2018, Volume 236, p. 408

For a graph G = (V,E), a Roman {2}-dominating function (R2DF) f : V → {0, 1, 2} has the property that for every vertex v ∈ V with f(v) = 0, either there exists...

Studies | Minimum weight | Numbers | Graphs | Trees (mathematics) | Independent sample

Studies | Minimum weight | Numbers | Graphs | Trees (mathematics) | Independent sample

Journal Article

Discrete mathematics, algorithms, and applications, ISSN 1793-8309, 09/2014, Volume 6, Issue 3, pp. np - np

Let G = (V, E) be a graph and let k be a positive integer. A Roman k-dominating function (Rk-DF) on G is a function f : V(G) arrow right {0, 1, 2} such that...

Functions (mathematics) | Integers | Graphs | Roman | Algorithms | Mathematical analysis

Functions (mathematics) | Integers | Graphs | Roman | Algorithms | Mathematical analysis

Journal Article

Discrete mathematics, algorithms, and applications, ISSN 1793-8309, 09/2014, Volume 6, Issue 3, pp. np - np

A Roman dominating function on a graph G is a function f : V(G) arrow right {0, 1, 2} satisfying the condition that every vertex u of G for which f(u) = 0 is...

Functions (mathematics) | Minimum weight | Trees | Construction | Algorithms | Mathematical analysis | Graphs | Roman

Functions (mathematics) | Minimum weight | Trees | Construction | Algorithms | Mathematical analysis | Graphs | Roman

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 2083-5892, 05/2013, Volume 33, Issue 2, pp. 337 - 346

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

strong equality | Roman domination | trees | independent Roman domination

strong equality | Roman domination | trees | independent Roman domination

Journal Article

Journal of Combinatorial Optimization, ISSN 1382-6905, 7/2015, Volume 30, Issue 1, pp. 27 - 33

...J Comb Optim (2015) 30:27–33
DOI 10.1007/s10878-013-9631-y
An algorithm for the dominator chromatic number
of a tree
Houcine Boumediene Merouane ·
Mustapha...

Trees | Dominator coloring | Dominating set | Mathematics | Theory of Computation | Optimization | Packing set | Convex and Discrete Geometry | Operations Research/Decision Theory | Mathematical Modeling and Industrial Mathematics | Combinatorics | 05C69 | 05C15 | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Algorithms

Trees | Dominator coloring | Dominating set | Mathematics | Theory of Computation | Optimization | Packing set | Convex and Discrete Geometry | Operations Research/Decision Theory | Mathematical Modeling and Industrial Mathematics | Combinatorics | 05C69 | 05C15 | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Algorithms

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 2016, Volume 204, pp. 22 - 28

In this paper, we initiate the study of a variant of Roman dominating functions. For a graph G=(V,E), a Roman {2}-dominating function f:V→{0,1,2} has the...

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

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

Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica, ISSN 1232-9274, 2011, Volume 31, Issue 2, pp. 153 - 158

For a graph \(G=(V,E)\), a set \(S\subseteq V\) is a dominating set if every vertex in \(V-S\) has at least a neighbor in \(S\). A dominating set \(S\) is a...

domination | global defensive alliance | global offensive alliance | trees

domination | global defensive alliance | global offensive alliance | trees

Journal Article

Discussiones Mathematicae. Graph Theory, ISSN 1234-3099, 2019, Volume 39, Issue 4, pp. 787 - 803

A total Roman dominating function on a graph G is a labeling f : V(G) ->{0, 1, 2} such that every vertex with label 0 has a neighbor with label 2 and the...

MATHEMATICS | total Roman reinforcement number | NUMBER | total Roman domination number | TOTAL DOMINATION | 05C69

MATHEMATICS | total Roman reinforcement number | NUMBER | total Roman domination number | TOTAL DOMINATION | 05C69

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 11/2019, Volume 270, pp. 159 - 167

A double Roman dominating function (DRDF) on a graph G=(V,E) is a function f:V→{0,1,2,3} having the property that if f(v)=0, then vertex v must have at least...

Domination | Roman domination | Double Roman domination number | MATHEMATICS, APPLIED | Minimum weight | Graphs | Mathematical functions | Questions | Apexes | Upper bounds

Domination | Roman domination | Double Roman domination number | MATHEMATICS, APPLIED | Minimum weight | Graphs | Mathematical functions | Questions | Apexes | Upper bounds

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 2019, Volume 257, pp. 1 - 11

A signed double Roman dominating function (SDRDF) on a graph G=(V,E) is a function f:V(G)→{−1,1,2,3} such that (i) every vertex v with f(v)=−1 is adjacent to...

Double Roman domination | Signed double Roman domination | Roman domination | MATHEMATICS, APPLIED | Minimum weight | Graphs | Mathematical functions | Trees (mathematics) | Apexes

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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