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arXiv · 2203.16619

The Gonality of Rook Graphs

Noah Speeter
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Abstract

Two dimensional rook graphs are the Cartesian product of two complete graphs. In this paper we prove that the gonality of these graphs is the expected value of $(n-1)m$ where $n$ is the size of the smaller complete graph and $m$ is the size of the larger. furthermore we compute the 2 and 3 gonalities of these graphs. We also explore the scramble number of these graphs, which is a new graph invariant and a lower bound on the gonality.

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Noah Speeter. 2022-05-20. The Gonality of Rook Graphs. https://arxiv.org/abs/2203.16619

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