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arXiv · 2410.10673

K5 and K3,3 are Toroidal Penny Graphs

Cédric Lorand
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Abstract

In this article we emphasize on the connection between two fields of study that are Penny Graphs, and the Optimal Packing of Spheres on the Flat Torus. We give a brief litterature overview on related results in the fields of planar graphs, penny graphs, toroidal penny graphs and spherical codes.We also show that $K5$ and $K_{3,3}$ are penny graphs on the flat square torus.

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Cédric Lorand. 2024-10-14. K5 and K3,3 are Toroidal Penny Graphs. https://arxiv.org/abs/2410.10673

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