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

Abstract

top
The paired domination number γ p r ( 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 p r ( π G ) = 2 γ p r ( G ) for all πG; γ p r ( K ₂ ☐ G ) = 2 γ p r ( G ) ; γ p r ( K ₂ ☐ G ) = γ p r ( G ) .

How to cite

top

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

top
  1. [1] B. Bresar, M.A. Henning and D.F. Rall, Paired-domination of Cartesian products of graphs, Util. Math. 73 (2007) 255-265. Zbl1161.05053
  2. [2] A.P. Burger and C.M. Mynhardt, Regular graphs are not universal fixers, Discrete Math. 310 (2010) 364-368, doi: 10.1016/j.disc.2008.09.016. Zbl1216.05098
  3. [3] A.P. Burger, C.M. Mynhardt and W.D. Weakley, On the domination number of prisms of graphs, Discuss. Math. Graph Theory 24 (2004) 303-318, doi: 10.7151/dmgt.1233. Zbl1064.05111
  4. [4] E.J. Cockayne, R.G. Gibson and C.M. Mynhardt, Claw-free graphs are not universal fixers, Discrete Math. 309 (2009) 128-133, doi: 10.1016/j.disc.2007.12.053. Zbl1219.05116
  5. [5] M. Edwards, R.G. Gibson, M.A. Henning and C.M. Mynhardt, On paired-domination edge critical graphs, Australasian J. Combin. 40 (2008) 279-292. Zbl1169.05032
  6. [6] R.G. Gibson, Bipartite graphs are not universal fixers, Discrete Math. 308 (2008) 5937-5943, doi: 10.1016/j.disc.2007.11.006. Zbl1181.05068
  7. [7] B.L. Hartnell and D.F. Rall, On Vizing's conjecture, Congr. Numer. 82 (1991) 87-96. Zbl0764.05092
  8. [8] B.L. Hartnell and D.F. Rall, On dominating the Cartesian product of a graph and K₂, Discuss. Math. Graph Theory 24 (2004) 389-402, doi: 10.7151/dmgt.1238. Zbl1063.05107
  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). 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.