Paired domination in prisms of graphs

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

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Abstract

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The paired domination number ${\gamma }_{pr}\left(G\right)$ 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: ${\gamma }_{pr}\left(\pi G\right)=2{\gamma }_{pr}\left(G\right)$ for all πG; ${\gamma }_{pr}\left(K₂☐G\right)=2{\gamma }_{pr}\left(G\right)$; ${\gamma }_{pr}\left(K₂☐G\right)={\gamma }_{pr}\left(G\right)$.

How to cite

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Christina 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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9. [9] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
10. [10] C.M. Mynhardt and Z. Xu, Domination in prisms of graphs: Universal fixers, Utilitas Math. 78 (2009) 185-201. Zbl1284.05199
11. [11] M. Schurch, Domination Parameters for Prisms of Graphs (Master's thesis, University of Victoria, 2005).

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