# Graphs, groups, and more: celebrating Brian Alspach’s 80th and Dragan Marušič’s 65th birthdays

28 May 2018 to 1 June 2018
Koper
UTC timezone

## Characterization of generalized Petersen graphs that are Kronecker covers

Not scheduled
15m
UP FHS (Koper)

### UP FHS

#### Koper

Titov trg 5,Koper

### 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)

### Presentation Materials

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