Speaker
Matjaž Krnc
(University of Primorska)
Description
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 $\mathrm{KC}(G)$ 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.
Primary authors
Matjaž Krnc
(University of Primorska)
Prof.
Tomaž Pisanski
(University of Primorska)
