Upper paired domination versus upper domination

@article{Alizadeh2021UpperPD,
  title={Upper paired domination versus upper domination},
  author={Hadi Alizadeh and Didem G{\"o}z{\"u}pek},
  journal={ArXiv},
  year={2021},
  volume={abs/2104.02446}
}
A paired dominating set $P$ is a dominating set with the additional property that $P$ has a perfect matching. While the maximum cardainality of a minimal dominating set in a graph $G$ is called the upper domination number of $G$, denoted by $\Gamma(G)$, the maximum cardinality of a minimal paired dominating set in $G$ is called the upper paired domination number of $G$, denoted by $\Gamma_{pr}(G)$. By Henning and Pradhan (2019), we know that $\Gamma_{pr}(G)\leq 2\Gamma(G)$ for any graph $G… 

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References

SHOWING 1-10 OF 28 REFERENCES

Graphs with large paired-domination number

TLDR
It is shown that there are exactly ten graphs that achieve equality in this bound and the (infinite family of) graphs that achieved equality inThis bound are characterized.

Paired-domination in generalized claw-free graphs

TLDR
It is shown that for every integer a ≥ 0, if G is a connected graphs-free graph of order n ≥ 2, then G is said to be F-free and this bound is sharp for graphs of arbitrarily large order.

A new lower bound on the domination number of a graph

TLDR
This paper characterize all trees T of order n and shows that if G is a connected graph of order, then all trees G achieving equality for this new bound are characterized.

The paired-domination and the upper paired-domination numbers of graphs

In this paper we continue the study of paired-domination in graphs. A paired-dominating set, abbreviated PDS, of a graph \(G\) with no isolated vertex is a dominating set of vertices whose induced

Upper total domination versus upper paired-domination

Let G be a graph with no isolated vertices. A set S of vertices in G is a total dominating set of G if every vertex of G is adjacent to some vertex in S, while a paired-dominating set of G is a

ALL GRAPHS WITH PAIRED-DOMINATION NUMBER TWO LESS THAN THEIR ORDER

Let \(G=(V,E)\) be a graph with no isolated vertices. A set \(S\subseteq V\) is a paired-dominating set of \(G\) if every vertex not in \(S\) is adjacent with some vertex in \(S\) and the subgraph

Total domination versus paired domination

TLDR
This paper proves several results on the ratio of these four parameters: for each r ≥ 2 the authors prove the sharp bound p/t ≤ 2−2/r for K1,r-free graphs.

Total Domination Versus Paired-Domination in Regular Graphs

TLDR
It is proved that for k ≥ 2 and k ≠ 57, if G has girth at least 5 and satisfies γpr(G)/γt(G) = (2k)/(k + 1), then it is shown that G is a diameter-2 Moore graph.

Algorithmic aspects of upper paired-domination in graphs

Paired versus double domination in K1,r-free graphs

TLDR
This paper shows that for r≥2, if G is a connected graph that does not contain K1,r as an induced subgraph, then γpr (G)≤γ×2(G) is the minimum cardinality of a double dominating set of G.