A note on domination and total domination in prisms

Wayne Goddard () and Michael A. Henning ()
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Wayne Goddard: Clemson University
Michael A. Henning: University of Johannesburg

Journal of Combinatorial Optimization, 2018, vol. 35, issue 1, No 2, 14-20

Abstract: Abstract Recently, Azarija et al. (Electron J Combin:1.19, 2017) considered the prism $$G \mathop {\square }K_2$$ G □ K 2 of a graph G and showed that $$\gamma _t(G \mathop {\square }K_2) = 2\gamma (G)$$ γ t ( G □ K 2 ) = 2 γ ( G ) if G is bipartite, where $$\gamma _t(G)$$ γ t ( G ) and $$\gamma (G)$$ γ ( G ) are the total domination number and the domination number of G. In this note, we give a simple proof and observe that there are similar results for other pairs of parameters. We also answer a question from that paper and show that for all graphs $$\gamma _t(G \mathop {\square }K_2) \ge \frac{4}{3}\gamma (G)$$ γ t ( G □ K 2 ) ≥ 4 3 γ ( G ) , and this bound is tight.

Keywords: Domination; Total domination; Prisms; 05C69; 05C76 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-017-0150-0

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