Paired domination in prisms of graphs

• Autorzy: Christina M. Mynhardt , Mark Schurch
• Języki publikacji: EN

Abstrakty

EN

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; $γ_{pr}(K₂☐ G) = 2γ_{pr}(G)$; $γ_{pr}(K₂☐ G) = γ_{pr}(G)$.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2011
• Tom: 31
• Numer: 1
• Strony: 5-23

Daty

wydano

2011

otrzymano

2009-01-29

poprawiono

2009-07-27

zaakceptowano

2009-07-27

Twórcy

autor

Christina M. Mynhardt

• Department of Mathematics and Statistics, University of Victoria, P.O. Box 3060 STN CSC, Victoria, BC, Canada V8W 3R4

autor

Mark Schurch

• Department of Mathematics and Statistics, University of Victoria, P.O. Box 3060 STN CSC, Victoria, BC, Canada V8W 3R4

Bibliografia

• [1] B. Bresar, M.A. Henning and D.F. Rall, Paired-domination of Cartesian products of graphs, Util. Math. 73 (2007) 255-265.
• [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.
• [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.
• [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.
• [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.
• [6] R.G. Gibson, Bipartite graphs are not universal fixers, Discrete Math. 308 (2008) 5937-5943, doi: 10.1016/j.disc.2007.11.006.
• [7] B.L. Hartnell and D.F. Rall, On Vizing's conjecture, Congr. Numer. 82 (1991) 87-96.
• [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.
• [9] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
• [10] C.M. Mynhardt and Z. Xu, Domination in prisms of graphs: Universal fixers, Utilitas Math. 78 (2009) 185-201.
• [11] M. Schurch, Domination Parameters for Prisms of Graphs (Master's thesis, University of Victoria, 2005).

Identyfikatory

DOI

10.7151/dmgt.1526