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Discussiones Mathematicae Graph Theory, 11/2019, Volume 39, Issue 4, pp. 829 - 839
The domination subdivision number sd(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in... 
domination | domination subdivision number | 05C99 | domination multisubdivision number | 05C69 | trees | 05C05 | computational complexity
Journal Article
Filomat, ISSN 0354-5180, 1/2016, Volume 30, Issue 8, pp. 2101 - 2110
A set 𝑋 is in 𝐺 if for any two vertices 𝑎,𝑏 ∈ 𝑋 there exists an 𝑎𝑏–geodesic such that all of its vertices belong to 𝑋. A set 𝑋 ⊆ 𝑉 is a if 𝑋 is... 
Integers | Numbers | Cardinality | Induced subgraphs | Discrete mathematics | Mathematics | Graph theory | Graphical subdivisions | Vertices | Weakly convex domination number | Weakly convex dominating set | Weakly convex domination subdivision number | MATHEMATICS | weakly convex dominating set | weakly convex domination number | MATHEMATICS, APPLIED | weakly convex domination subdivision number
Journal Article
Opuscula Mathematica, ISSN 1232-9274, 2016, Volume 36, Issue 5, pp. 575 - 588
Given a graph \(G=(V,E)\), the subdivision of an edge \(e=uv\in E(G)\) means the substitution of the edge \(e\) by a vertex \(x\) and the new edges \(ux\) and... 
Domination | Edge multisubdivision | Independent domination | Paired domination | Corona graph | Edge subdivision | independent domination | domination | edge multisubdivision | edge subdivision | corona graph | paired domination
Journal Article
AKCE International Journal of Graphs and Combinatorics, ISSN 0972-8600, 2018
Imagine that we are given a set D of officials and a set W of civils. For each civil x∈W, there must be an official v∈D that can serve x, and whenever any such... 
Domination | Nordhaus–Gaddum | Corona | Certified domination
Journal Article
Opuscula Mathematica, ISSN 1232-9274, 2019, Volume 39, Issue 6, pp. 815 - 827
A set \(D\) of vertices of a graph \(G=(V_G,E_G)\) is a dominating set of \(G\) if every vertex in \(V_G-D\) is adjacent to at least one vertex in \(D\). The... 
certified domination | domination
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2018, Volume 38, Issue 2, pp. 573 - 586
A subset of vertices of a graph is a dominating set of if every vertex not in has a neighbor in , while is a total dominating set of if every vertex has a... 
domination | 05C99 | 05C69 | paired-domination | total domination | Domination | Paired-domination | Total domination | MATHEMATICS
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 08/2016, Volume 36, Issue 3, pp. 661 - 668
We consider (ψ −γ )-perfect graphs, i.e., graphs G for which ψ (H) = γ (H) for any induced subgraph H of G, where ψ and γ are the k-path vertex cover number... 
k-path vertex cover | perfect graphs | distance k-domination number | Distance k-domination number | K-path vertex cover | Perfect graphs | MATHEMATICS | DOMINATION
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 1/2018, Volume 34, Issue 1, pp. 261 - 276
A dominating set in a graph G is a set S of vertices of G such that every vertex not in S has a neighbor in S. Further, if every vertex of G has a neighbor in... 
Upper total domination number | Total domination number | Cubic graph | Domination number | Mathematics | Engineering Design | Combinatorics | Upper domination number | MATHEMATICS | NUMBER | HYPERGRAPHS
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2015, Volume 35, Issue 2, pp. 315 - 327
The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be... 
(total) domination subdivision number | (total) domination multisubdivision number | trees | (total) domination | Trees | MATHEMATICS | SUBDIVISION NUMBERS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 04/2014, Volume 167, pp. 94 - 99
The bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number... 
Domination | Bondage number | Strong product graphs | Direct product graphs | PLANAR GRAPHS | MATHEMATICS, APPLIED | Bonding strength | Graphs | Mathematical analysis | Bonding | Mathematics - Combinatorics
Journal Article
02/2020
A subset $D$ of $V$ is \emph{dominating} in $G$ if every vertex of $V-D$ has at least one neighbour in $D;$ let $\gamma(G)$ be the minimum cardinality among... 
Mathematics - Combinatorics
Journal Article
11/2019
Given a graph $G=(V(G), E(G))$, the size of a minimum dominating set, minimum paired dominating set, and a minimum total dominating set of a graph $G$ are... 
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 2019, Volume 39, Issue 4, p. 829
Journal Article
02/2019
In this paper we study relations between connected and weakly convex domination numbers. We show that in general the difference between these numbers can be... 
Mathematics - Combinatorics
Journal Article
Australasian Journal of Combinatorics, ISSN 1034-4942, 06/2012, Volume 53, pp. 19 - 30
Journal Article
Australasian Journal of Combinatorics, ISSN 1034-4942, 2010, Volume 47, pp. 269 - 277
Journal Article
06/2016
Imagine that we are given a set $D$ of officials and a set $W$ of civils. For each civil $x \in W$, there must be an official $v \in D$ that can serve $x$, and... 
Mathematics - Combinatorics
Journal Article
03/2016
In this paper, for a graph G and a family of partitions P of vertex neighborhoods of G, we define the general corona G \circ P of G. Among several properties... 
Mathematics - Combinatorics
Journal Article
10/2017
A set $D$ of vertices of a graph $G$ is a dominating set of $G$ if every vertex in $V_G-D$ is adjacent to at least one vertex in $D$. The domination number... 
Mathematics - Combinatorics
Journal Article
10/2013
The \emph{domination subdivision number} sd$(G)$ of a graph $G$ is the minimum number of edges that must be subdivided (where an edge can be subdivided at most... 
Mathematics - Combinatorics
Journal Article
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