The Gonality of Rook Graphs

Noah Speeter

The Gonality of Rook Graphs

Combinatorics 2022-05-24 v2 Algebraic Geometry

Authors: Noah Speeter

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.

Keywords

graph theory graph pebbling random graphs

Cite

@article{arxiv.2203.16619,
  title  = {The Gonality of Rook Graphs},
  author = {Noah Speeter},
  journal= {arXiv preprint arXiv:2203.16619},
  year   = {2022}
}

Comments

10 pages, 7 figures

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