On integer radii coin representations of the wheel graph

2010/05/19 by Geir Agnarsson, Agnarsson, Geir, Jill Bigley Dunham +1
Mathematics · #05C10 #05C25 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications #math.AC #math.CO #msc:05C10 #msc:05C25

paper · pdf · doi:10.48550/arxiv.1005.3515

26 pages, 2 figures

arxiv created 2010/05/19 · openalex publication_date 2010/05/19 · arxiv updated 2010/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A \em flower is a coin graph representation of the wheel graph. A \em petal of the wheel graph is an edge to the center vertex. In this paper we investigate flowers whose coins have integer radii. For an n-petaled flower we show there is a unique irreducible polynomial P_n in n variables over the integers \ints, the affine variety of which contains the cosines of the internal angles formed by the petals of the flower. We also establish a recursion that these irreducible polynomials satisfy. Using the polynomials P_n, we develop a parameterization for all the integer radii of the coins of the 3-petal flower.

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