Complexity properties of complementary prisms

The complementary prism (Gbar{G}) of a graph G arises from the disjoint union of the graph G and its complement (bar{G}) by adding the edges of a perfect matching joining pairs of corresponding vertices of G and (bar{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)-convexity. We establish hardness results and identify some efficiently solvable cases.