Abstract
Recently, Azarija et al. (Electron J Combin:1.19, 2017) considered the prism $$G \mathop {\square }K_2$$ of a graph G and showed that $$\gamma _t(G \mathop {\square }K_2) = 2\gamma (G)$$ if G is bipartite, where $$\gamma _t(G)$$ and $$\gamma (G)$$ 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 $$\gamma _t(G \mathop {\square }K_2) \ge \frac{4}{3}\gamma (G)$$ , and this bound is tight.
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