2006/09/13 by Eberhard H.-A. Gerbracht, Gerbracht, Eberhard H. -A.
Computer Science · Mathematics · #05C10 #05C62 (Primary) #13P10 (Secondary) #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #FOS: Mathematics #Mathematics and Applications #Point processes and geometric inequalities #Symbolic Computation (cs.SC)
paper · pdf · doi:10.48550/arxiv.math/0609360
openalex publication_date 2006/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.