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by Chartrand and Gary and Haynes and Teresa W and Henning and Michael A and Zhang and Ping
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Journal Article
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