Abstract
An odd wheel graph is a graph formed by connecting a new vertex to all vertices of an odd cycle. We answer a question of Rosenfeld and Le by showing that odd wheels cannot be drawn in the plane such that the lengths of the edges are odd integers.
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Notes
- 1.
There is some discrepancy in the literature, since some authors prefer to denote by \(W_n\) the wheel graph on n vertices.
References
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Acknowledgement
We would like to thank SciExperts for providing free access to the software Wolfram Mathematica, and therefore to the database of Ed Pegg Jr. [7] on embeddings of wheels. We also thank Dömötör Pálvölgyi and our anonymous reviewers for valuable suggestions and encouragement.
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Damásdi, G. (2020). Odd Wheels Are Not Odd-distance Graphs. In: Auber, D., Valtr, P. (eds) Graph Drawing and Network Visualization. GD 2020. Lecture Notes in Computer Science(), vol 12590. Springer, Cham. https://doi.org/10.1007/978-3-030-68766-3_10
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