Graphs with Cayley canonical double covers

A canonical double cover B(X) of a graph X is the direct product of X and the complete graph K-2 on two vertices. In order to answer the question when a canonical double cover of a given graph is a Cayley graph, in 1992 Marusic et al. introduced the concept of generalized Cayley graphs. In this paper this concept is generalized to a wider class of graphs, the so-called extended generalized Cayley graphs. It is proved that the canonical double cover of a connected non-bipartite graph X is a Cayley graph if and only if X is an extended generalized Cayley graph. This corrects an incorrectly stated claim in [Discrete Math. 102 (1992), 279-285]. (C) 2019 Elsevier B.V. All rights reserved.