Minimal Polynomials for the Coordinates of the Harborth Graph
<|reference_start|>Minimal Polynomials for the Coordinates of the Harborth Graph: The Harborth graph is the smallest known example of a 4-regular planar unit-distance graph. In this paper we give an analytical description of the coordinates of its vertices for a particular embedding in the Euclidean plane. More precisely, we show, how to calculate the minimal polynomials of the coordinates of its vertices (with the help of a computer algebra system), and list those. Furthermore some algebraic properties of these polynomials, and consequences to the structure of the Harborth graph are determined.<|reference_end|>
@article{gerbracht2006minimal,
    title={Minimal Polynomials for the Coordinates of the Harborth Graph},
    author={Eberhard H.-A. Gerbracht},
    journal={arXiv preprint arXiv:math/0609360},
    year={2006},
    archivePrefix={arXiv},
    eprint={math/0609360},
    primaryClass={math.CO cs.SC}
}