The core of a vertex transitive complementary prism of a lexicographic product

The complementary prism of a graph Γ is the ΓΓ̄, which formed from union and its complement Γ̄ by adding an edge between each pair identical vertices in Γ̄. Vertex-transitive self-complementary graphs provide vertex-transitive prisms. It was recently proved author that ΓΓ̄ core, i.e. all endomorphisms are automorphisms, whenever vertex-transitive, self-complementary, either core or complete graph. In this paper same conclusion obtained for some other classes can be decomposed as lexicographic product = Γ1[Γ2]. process new results about homomorphisms obtained.