Abstract
Let G be a graph and \({\overline {G}}\) be the complement of G. The complementary prism \(G{\overline {G}}\) of G is the graph formed from the disjoint union of G and \({\overline {G}}\) by adding the edges of a perfect matching between the corresponding vertices of G and \({\overline {G}}\) . For example, if G is a 5-cycle, then \(G{\overline {G}}\) is the Petersen graph. In this paper we consider domination and total domination numbers of complementary prisms. For any graph G, \(\max\{\gamma(G),\gamma({\overline {G}})\}\le \gamma(G{\overline {G}})\) and \(\max\{\gamma_{t}(G),\gamma_{t}({\overline {G}})\}\le \gamma_{t}(G{\overline {G}})\) , where γ(G) and γ t (G) denote the domination and total domination numbers of G, respectively. Among other results, we characterize the graphs G attaining these lower bounds.
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Research supported in part by the South African National Research Foundation and the University of KwaZulu-Natal.
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Haynes, T.W., Henning, M.A. & van der Merwe, L.C. Domination and total domination in complementary prisms. J Comb Optim 18, 23–37 (2009). https://doi.org/10.1007/s10878-007-9135-8
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DOI: https://doi.org/10.1007/s10878-007-9135-8