The core of a vertex-transitive complementary prism - Orel, Marko (Ars mathematica contemporanea, 2023)
The complementary prism ?$Γ \overline{Γ}$? is obtained from the union of a graph ?$Γ$? and its complement ?$\overline{Γ}$? where each pair of identical vertices in ?$Γ$? and ?$\overline{Γ}$? is joined by an edge. It generalizes the Petersen graph, which is the complementary prism of the pentagon. The core of a vertex-transitive complementary prism is studied. In particular, it is shown that a vertex-transitive complementary prism ?$Γ \overline{Γ}$? is a core, i.e. all its endomorphisms are automorphisms, whenever ?$Γ$? is a core or its core is a complete graph.
Keywords: complementary prism; core; graph homomorphism; homomorfizmi grafov; jedra; komplementarne prizme; sebikomplementarni grafi; self-complementary graph; točkovno tranzitivni grafi; vertex-transitive graph