Minimal Polynomials for the Coordinates of the Harborth Graph
| dc.creator | Gerbracht, Eberhard H. -A. | |
| dc.date | 2006-09-13 | |
| dc.date | 2007-01-24 | |
| dc.date.accessioned | 2026-07-07T08:30:56Z | |
| dc.date.available | 2026-07-07T08:30:56Z | |
| dc.description | 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. | |
| dc.description | v1: documentclass amsart, 16 pages, 4 figures. v2: same as v1, but now has 18 pages, with a final section ("Coda") on the consequences to the structure of the Harborth graph and some references added; some typos corrected. v3: minor change to the introduction (re: history of the Harborth Graph); one reference added; some more typos corrected | |
| dc.identifier | https://arxiv.org/abs/math/0609360 | |
| dc.identifier | http://arxiv.org/abs/math/0609360 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138372 | |
| dc.subject | Combinatorics | |
| dc.subject | Symbolic Computation | |
| dc.subject | 05C62 (Primary); 05C10, 13P10 (Secondary) | |
| dc.title | Minimal Polynomials for the Coordinates of the Harborth Graph | |
| dc.type | text |