Abstract
The complementary prism $$G\bar{G}$$GG? of a graph G arises from the disjoint union of the graph G and its complement $$\bar{G}$$G? by adding the edges of a perfect matching joining pairs of corresponding vertices of G and $$\bar{G}$$G?. Haynes, Henning, Slater, and van der Merwe introduced the complementary prism and as a variation of the well-known prism. We study algorithmic/complexity properties of complementary prisms with respect to cliques, independent sets, k-domination, and especially $$P_3$$P3-convexity. We establish hardness results and identify some efficiently solvable cases.
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