# Characterization of generalised Petersen graphs that are Kronecker covers

## Main Article Content

## Abstract

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.

## Article Details

How to Cite

Krnc, M., & Pisanski, T.
(2019).
Characterization of generalised Petersen graphs that are Kronecker covers.

*Acta Mathematica Universitatis Comenianae, 88*(3), 891-895. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1230/741
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Section

EUROCOMB 2019