Generalized Petersen graphs and Kronecker covers

Matjaž Krnc (1, 2, 3) , Tomaž Pisanski (1)

1 FAMNIT - Faculty of Mathematics, Natural Sciences and Information Technologies [Koper]
2 FMF - Faculty of Mathematics and Physics [Ljubljana]
3 IMFM

The family of generalized Petersen graphs $G(n,k)$, introduced by Coxeter et al. [4] and named by Mark Watkins (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 a special type of bipartite covering graph of $G$, isomorphic to the direct (tensor) product of $G$ and $K_2$. We characterize all the members of generalized Petersen graphs that are Kronecker covers, and describe the structure of their respective quotients. We observe that some of such quotients are again generalized 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.

Mots clés: Generalized Petersen graphs; Kronecker cover; generalised Petersen graphs

Domaines: Combinatoire [math.CO]

Matjaž Krnc, Tomaž Pisanski. Generalized Petersen graphs and Kronecker covers. Discrete Mathematics and Theoretical Computer Science, In press, vol. 21 no. 4, ⟨10.23638/DMTCS-21-4-15⟩. ⟨hal-01804033v6⟩