A note on domination and total domination in prisms |
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| Authors: | Wayne Goddard Michael A. Henning |
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| Affiliation: | 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) = 2gamma (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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