Geodesic
Characterization of generalised Petersen graphs that are Kronecker covers
Matjaž Krnc1 ; Tomaž Pisanski1 ; Matjaž Krnc ; Tomaž Pisanski
1Faculty of Mathematics, Natural Sciences and Information Technologies University of Primorska, Koper, Slovenia
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 891-895 
Matjaž Krnc; Tomaž Pisanski; Matjaž Krnc; Tomaž Pisanski. Characterization of generalised Petersen graphs  that are Kronecker covers. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 891-895. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a82/
@article{AMUC_2019_88_3_a82,
     author = {Matja\v{z} Krnc and Toma\v{z} Pisanski and Matja\v{z} Krnc and Toma\v{z} Pisanski},
     title = { Characterization of generalised {Petersen} graphs  that are {Kronecker} covers},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {891--895},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a82/}
}
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Voir la notice de l'article provenant de la source Comenius University

The family of generalised Petersen graphs $G\left(n,k\right)$, introduced by Coxeter (1950) and named by 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 $\mathrm{KC}\left(G\right)$ 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.