A note on domination and total domination in prisms |
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| Authors: | Wayne Goddard Michael A Henning |
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| Institution: | 1.School of Computing and Department of Mathematical Sciences,Clemson University,Clemson,USA;2.Department of Pure and Applied Mathematics,University of Johannesburg,Auckland Park,South Africa |
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| 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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