## Displaying similar documents to “Minimal acyclic dominating sets and cut-vertices”

### Vizing-like conjecture for the upper domination of Cartesian products of graphs -- the proof.

The Electronic Journal of Combinatorics [electronic only]

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### Graphs with disjoint dominating and paired-dominating sets

Open Mathematics

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A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a paired-dominating set of a graph is a dominating set such that the subgraph induced by the dominating set contains a perfect matching. In this paper, we show that no minimum degree is sufficient to guarantee the existence of a disjoint dominating set and a paired-dominating set. However, we prove that the vertex set of every cubic graph can be partitioned...

### Disconnected neighbourhood graphs

Mathematica Slovaca

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### Total domination subdivision numbers of graphs

Discussiones Mathematicae Graph Theory

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A set S of vertices in a graph G = (V,E) is a total dominating set of G if every vertex of V is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set of G. The total domination subdivision number of G is the minimum number of edges that must be subdivided (where each edge in G can be subdivided at most once) in order to increase the total domination number. First we establish bounds on the total domination subdivision number...

### The Domination Number of K 3 n

Discussiones Mathematicae Graph Theory

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Let K3n denote the Cartesian product Kn□Kn□Kn, where Kn is the complete graph on n vertices. We show that the domination number of K3n is [...]

### Two Short Proofs on Total Domination

Discussiones Mathematicae Graph Theory

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A set of vertices of a graph G is a total dominating set if each vertex of G is adjacent to a vertex in the set. The total domination number of a graph Υt (G) is the minimum size of a total dominating set. We provide a short proof of the result that Υt (G) ≤ 2/3n for connected graphs with n ≥ 3 and a short characterization of the extremal graphs.

### On a quasiordering of bipartite graphs.

Publications de l'Institut Mathématique. Nouvelle Série

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### A new upper bound on the total domination number of a graph.

The Electronic Journal of Combinatorics [electronic only]

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