Generalized Petersen Graphs and Kronecker Covers

The family of generalised Petersen graphs G(n, k), introduced by Coxeter et al. [4] and named byWatkins (1969), is a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding vertices of a star polygon. The Kronecker cover KC(G) of a simple undirected graph G is a special type of bipartite covering graph of G, isomorphic to the direct (tensor) product of G and K-2. We characterize all generalised Petersen graphs that are Kronecker covers, and describe the structure of their respective quotients. We observe that some of such quotients are again generalised Petersen graphs, and describe all such pairs. The results of this paper have been presented at EUROCOMB 2019 and an extended abstract has been published elsewhere.