The core of a complementary prism

Abstract

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