# Paired domination in prisms of graphs

Christina M. Mynhardt; Mark Schurch

Discussiones Mathematicae Graph Theory (2011)

- Volume: 31, Issue: 1, page 5-23
- ISSN: 2083-5892

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topChristina M. Mynhardt, and Mark Schurch. "Paired domination in prisms of graphs." Discussiones Mathematicae Graph Theory 31.1 (2011): 5-23. <http://eudml.org/doc/270903>.

@article{ChristinaM2011,

abstract = {The paired domination number $γ_\{pr\}(G)$ of a graph G is the smallest cardinality of a dominating set S of G such that ⟨S⟩ has a perfect matching. The generalized prisms πG of G are the graphs obtained by joining the vertices of two disjoint copies of G by |V(G)| independent edges. We provide characterizations of the following three classes of graphs: $γ_\{pr\}(πG) = 2γ_\{pr\}(G)$ for all πG; $γ_\{pr\}(K₂☐ G) = 2γ_\{pr\}(G)$; $γ_\{pr\}(K₂☐ G) = γ_\{pr\}(G)$.},

author = {Christina M. Mynhardt, Mark Schurch},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {domination; paired domination; prism of a graph; Cartesian product},

language = {eng},

number = {1},

pages = {5-23},

title = {Paired domination in prisms of graphs},

url = {http://eudml.org/doc/270903},

volume = {31},

year = {2011},

}

TY - JOUR

AU - Christina M. Mynhardt

AU - Mark Schurch

TI - Paired domination in prisms of graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2011

VL - 31

IS - 1

SP - 5

EP - 23

AB - The paired domination number $γ_{pr}(G)$ of a graph G is the smallest cardinality of a dominating set S of G such that ⟨S⟩ has a perfect matching. The generalized prisms πG of G are the graphs obtained by joining the vertices of two disjoint copies of G by |V(G)| independent edges. We provide characterizations of the following three classes of graphs: $γ_{pr}(πG) = 2γ_{pr}(G)$ for all πG; $γ_{pr}(K₂☐ G) = 2γ_{pr}(G)$; $γ_{pr}(K₂☐ G) = γ_{pr}(G)$.

LA - eng

KW - domination; paired domination; prism of a graph; Cartesian product

UR - http://eudml.org/doc/270903

ER -

## References

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- [11] M. Schurch, Domination Parameters for Prisms of Graphs (Master's thesis, University of Victoria, 2005).

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