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The family of generalized Petersen graphs $G(n, k)$, introduced by Coxeter etal. [4] and named by Mark Watkins (1969), is a family of cubic graphs formed byconnecting the vertices of a regular polygon to the corresponding vertices of astar polygon. The Kronecker cover $\mathrm{KC}(G)$ of a simple undirected graph$G$ is a a special type of bipartite covering graph of $G$, isomorphic to thedirect (tensor) product of $G$ and $K_2$. We characterize all the members ofgeneralized Petersen graphs that are Kronecker covers, and describe thestructure of their respective quotients. We observe that some of such quotientsare again generalized Petersen graphs, and describe all such pairs.

Characterization of generalized Petersen graphs that are Kronecker covers