The core of a complementary prism

Abstract

AbstractThe complementary prism $$\Gamma {\bar{\Gamma }}$$ Γ Γ ¯ is constructed from the disjoint union of a graph $$\Gamma $$ Γ and its complement $${\bar{\Gamma }}$$ Γ ¯ if an edge is added between each pair of identical vertices in $$\Gamma $$ Γ and $${\bar{\Gamma }}$$ Γ ¯ . It generalizes the Petersen graph, which is obtained if $$\Gamma $$ Γ is the pentagon. The core of the complementary prism is investigated for arbitrary simple graph $$\Gamma $$ Γ . In particular, it is shown that if $$\Gamma $$ Γ is strongly regular and self-complementary, then $$\Gamma {\bar{\Gamma }}$$ Γ Γ ¯ is a core, i.e. all its endomorphisms are automorphisms.