The core of a vertex-transitive complementary prism

Abstract

The complementary prism ΓΓ̄  is obtained from the union of a graph Γ and its complement Γ̄ where each pair of identical vertices in Γ and Γ̄  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 ΓΓ̄  is a core, i.e. all its endomorphisms are automorphisms, whenever Γ is a core or its core is a complete graph.