Paired domination in prisms of graphs

Christina Mynhardt; Mark Schurch

ArticleOriginal scientific text

Title

Paired domination in prisms of graphs

Authors ¹, ¹

Affiliations

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

Abstract

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)

.

Keywords

ENG

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

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Title

Paired domination in prisms of graphs

Affiliations

Abstract

Keywords

Bibliography