On integer radii coin representations of the wheel graph

Details On integer radii coin representations of the wheel graph On integer radii coin representations of the wheel graph

2010-05-19

arxiv.org/abs/1005.3515v1

Mathematics

Commutative Algebra

26 pages, 2 figures

Scientific paper

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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