Let G be a graph and
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be the complement of G. The complementary prism
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of G is the graph formed from the disjoint union of G and
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by adding the edges of a perfect matching between the corresponding vertices of G and
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. For example, if G is a 5-cycle, then
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is the Petersen graph. In this paper we consider domination and total domination numbers of complementary prisms. For any graph G,
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\begin{document}$\max\{\gamma(G),\gamma({\overline {G}})\}\le \gamma(G{\overline {G}})$\end{document}
and
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\begin{document}$\max\{\gamma_{t}(G),\gamma_{t}({\overline {G}})\}\le \gamma_{t}(G{\overline {G}})$\end{document}
, where γ(G) and γt(G) denote the domination and total domination numbers of G, respectively. Among other results, we characterize the graphs G attaining these lower bounds.
