2019, SpringerBriefs in Mathematics, ISBN 9783030311094, 100

This book is in honor of the 80th birthday of Stephen Hedetniemi. It describes advanced material in graph theory in the areas of domination, coloring, spanning...

Graph theory | Graph Theory | Mathematics

Graph theory | Graph Theory | Mathematics

eBook

Discussiones Mathematicae Graph Theory, 08/2019, Volume 39, Issue 3, pp. 659 - 671

Let be a graph with vertex set and no isolated vertices. A sub-set ⊆ is a semipaired dominating set of if every vertex in \ is adjacent to a vertex in and can...

semipaired domination | 05C69 | paired-domination

semipaired domination | 05C69 | paired-domination

Journal Article

1998, 1, Monographs and textbooks in pure and applied mathematics, ISBN 0824700341, Volume 209., xii, 497

""Presents the latest in graph domination by leading researchers from around the world-furnishing known results, open research problems, and proof techniques....

Domination (Graph theory) | Applied Mathematics

Domination (Graph theory) | Applied Mathematics

Book

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

1998, Monographs and textbooks in pure and applied mathematics, ISBN 9780824700331, Volume 208, xi, 446

Book

Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 4/2016, Volume 10, Issue 1, pp. 65 - 72

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

Discrete mathematics | Differentials | Mathematical functions | Mathematical minima | Vertices | Roman domination | Independent domination | Total domination | Ve-domination | MATHEMATICS | MATHEMATICS, APPLIED | vedomination | independent domination | total domination | GRAPHS

Discrete mathematics | Differentials | Mathematical functions | Mathematical minima | Vertices | Roman domination | Independent domination | Total domination | Ve-domination | MATHEMATICS | MATHEMATICS, APPLIED | vedomination | independent domination | total domination | GRAPHS

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2019, Volume 39, Issue 2, pp. 575 - 588

Let be a graph with vertex set and a distribution of pebbles on the vertices of . A pebbling move consists of removing two pebbles from a vertex and placing...

restricted optimal pebbling | 05C78 | graph rubbling | optimal rubbling | graph pebbling | MATHEMATICS | GRAHAMS PEBBLING CONJECTURE | NUMBER | PRODUCTS | t-restricted optimal pebbling

restricted optimal pebbling | 05C78 | graph rubbling | optimal rubbling | graph pebbling | MATHEMATICS | GRAHAMS PEBBLING CONJECTURE | NUMBER | PRODUCTS | t-restricted optimal pebbling

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 07/2016, Volume 207, pp. 39 - 44

A (closed) neighborhood-restricted [≤2]-coloring of a graph G is an assignment of colors to the vertices of G such that no more than two colors are assigned in...

Coloring | [formula omitted]-achromatic number | Neighborhood-restricted colorings | Chromatic number | [≤k]-achromatic number | [≤2]-achromatic number | [<= 2]-achromatic number | MATHEMATICS, APPLIED | [<= k]-achromatic number | Graphs | Graph theory | Upper bounds | Mathematical analysis

Coloring | [formula omitted]-achromatic number | Neighborhood-restricted colorings | Chromatic number | [≤k]-achromatic number | [≤2]-achromatic number | [<= 2]-achromatic number | MATHEMATICS, APPLIED | [<= k]-achromatic number | Graphs | Graph theory | Upper bounds | Mathematical analysis

Journal Article

Thorax, ISSN 0040-6376, 09/2015, Volume 70, Issue 9, pp. 822 - 829

BackgroundThere is limited data on the risk factors and phenotypical characteristics associated with spirometrically confirmed COPD in never-smokers in the...

DIAGNOSIS | OBSTRUCTIVE PULMONARY-DISEASE | NONSMOKERS | RESPIRATORY SYSTEM | CITIES | SMOKING | PREVALENCE | HEALTH | GENDER-DIFFERENCES | AIR-FLOW OBSTRUCTION | DECLINE | Smoking - adverse effects | Prevalence | Prospective Studies | Cross-Sectional Studies | Humans | Middle Aged | Risk Factors | Airway Obstruction - physiopathology | Logistic Models | Male | Hospitalization | Lung - physiopathology | Pulmonary Disease, Chronic Obstructive - physiopathology | Canada | Tobacco Smoke Pollution - adverse effects | Adult | Female | Aged | CT imaging | Lung diseases, Obstructive | Care and treatment | Usage | Smokers | Clinical trials | Health aspects | Observational studies

DIAGNOSIS | OBSTRUCTIVE PULMONARY-DISEASE | NONSMOKERS | RESPIRATORY SYSTEM | CITIES | SMOKING | PREVALENCE | HEALTH | GENDER-DIFFERENCES | AIR-FLOW OBSTRUCTION | DECLINE | Smoking - adverse effects | Prevalence | Prospective Studies | Cross-Sectional Studies | Humans | Middle Aged | Risk Factors | Airway Obstruction - physiopathology | Logistic Models | Male | Hospitalization | Lung - physiopathology | Pulmonary Disease, Chronic Obstructive - physiopathology | Canada | Tobacco Smoke Pollution - adverse effects | Adult | Female | Aged | CT imaging | Lung diseases, Obstructive | Care and treatment | Usage | Smokers | Clinical trials | Health aspects | Observational studies

Journal Article

2018, Problem Books in Mathematics, ISBN 3319976842, 1

This second volume in a two-volume series provides an extensive collection of conjectures and open problems in graph theory. It is designed for both graduate...

Linear and Multilinear Algebras, Matrix Theory | Mathematics | History of Mathematical Sciences | Combinatorics | Graph Theory

Linear and Multilinear Algebras, Matrix Theory | Mathematics | History of Mathematical Sciences | Combinatorics | Graph Theory

eBook

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

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 10/2017, Volume 40, Issue 4, pp. 1443 - 1454

...Bull. Malays. Math. Sci. Soc. (2017) 40:1443–1454 DOI 10.1007/s40840-015-0141-1 Mixed Roman Domination in Graphs H. Abdollahzadeh Ahangar 1 · Teresa W. Haynes...

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

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

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 11/2018, Volume 38, Issue 4, pp. 1007 - 1021

Let be a nontrivial connected, edge-colored graph. An edge-cut of is called a rainbow cut if no two edges in are colored the same. An edge-coloring of is a...

rainbow disconnection | edge coloring | rainbow connection | 05C40 | 05C15 | Rainbow connection | Rainbow disconnection | Edge coloring | MATHEMATICS

rainbow disconnection | edge coloring | rainbow connection | 05C40 | 05C15 | Rainbow connection | Rainbow disconnection | Edge coloring | MATHEMATICS

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2018, Volume 38, Issue 1, pp. 203 - 215

A dominating set in a graph is a set of vertices such that every vertex in ( ) \ is adjacent to at least one vertex in , and the domination number of is the...

domination | connected domination | clique domination | complement | 05C69 | restrained domination | total domination | Domination | Connected domination | Complement | Clique domination | Total domination | Restrained domination | MATHEMATICS | NUMBER

domination | connected domination | clique domination | complement | 05C69 | restrained domination | total domination | Domination | Connected domination | Complement | Clique domination | Total domination | Restrained domination | MATHEMATICS | NUMBER

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

AKCE International Journal of Graphs and Combinatorics, ISSN 0972-8600, 11/2015, Volume 12, Issue 2-3, pp. 155 - 160

For a graph G=(V,E) and a set of vertices S⊆V, a vertex v∈S is said to be very cost effective if it is adjacent to more vertices in V∖S than in S. A...

Very cost effective bipartition | Cost effective bipartition

Very cost effective bipartition | Cost effective bipartition

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 9/2015, Volume 31, Issue 5, pp. 1163 - 1176

... Three and Many Dominating Pairs Camino Balbuena · Adriana Hansberg · Teresa W. Haynes · Michael A. Henning Received: 1 December 2013 / Revised: 14 June 2014...

Domination | 05C65 | Bull-free | Diameter-2-critical | Total domination edge critical | Mathematics | Engineering Design | Combinatorics | 05C69 | Diameter critical | COMPLEMENTS | SIMON | DIAMETER-2-CRITICAL GRAPHS | MURTY | CONJECTURE | MATHEMATICS | PERFECT | DIAMETER 2-CRITICAL GRAPHS | Resveratrol | Graph representations | Graphs

Domination | 05C65 | Bull-free | Diameter-2-critical | Total domination edge critical | Mathematics | Engineering Design | Combinatorics | 05C69 | Diameter critical | COMPLEMENTS | SIMON | DIAMETER-2-CRITICAL GRAPHS | MURTY | CONJECTURE | MATHEMATICS | PERFECT | DIAMETER 2-CRITICAL GRAPHS | Resveratrol | Graph representations | Graphs

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 11/2016, Volume 36, Issue 4, pp. 1043 - 1050

A set S of vertices of a graph G is a dominating set if every vertex not in S is adjacent to a vertex of S and is a total dominating set if every vertex of G...

domination | nontotal dominating partition | non-dominating partition | total domination | Domination | Non-dominating partition | Total domination | Non-total dominating partition | MATHEMATICS | non-total dominating partition

domination | nontotal dominating partition | non-dominating partition | total domination | Domination | Non-dominating partition | Total domination | Non-total dominating partition | MATHEMATICS | non-total dominating partition

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

Central European Journal of Mathematics, ISSN 1895-1074, 12/2014, Volume 12, Issue 12, pp. 1882 - 1889

... for diameter-2-critical graphs Research Article Teresa W. Haynes 1,2∗ , Michael A. Henning 2y , Lucas C. van der Merwe 3z , Anders Yeo 2,4x 1 Department of Mathematics and Statistics...

Geometry | 05C65 | Algebra | Topological Groups, Lie Groups | Diameter-2-critical | Total domination critical | Mathematics, general | Probability Theory and Stochastic Processes | Mathematics | Number Theory | Diameter critical | MATHEMATICS | SIMON | EDGE CRITICAL GRAPHS | MURTY | DIAMETER 2-CRITICAL GRAPHS | TOTAL DOMINATION | CONJECTURE

Geometry | 05C65 | Algebra | Topological Groups, Lie Groups | Diameter-2-critical | Total domination critical | Mathematics, general | Probability Theory and Stochastic Processes | Mathematics | Number Theory | Diameter critical | MATHEMATICS | SIMON | EDGE CRITICAL GRAPHS | MURTY | DIAMETER 2-CRITICAL GRAPHS | TOTAL DOMINATION | CONJECTURE

Journal Article

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