On the Gonality of Ferrers Rook Graphs
David Jensen, Marissa Morvai, William Welch, Sydney Yeomans

TL;DR
This paper investigates the gonality of Ferrers rook graphs, proposing a conjectural formula, proving it for specific families and small cases, advancing understanding of their algebraic and combinatorial properties.
Contribution
It introduces a conjectural formula for the gonality of Ferrers rook graphs and proves it for certain infinite families and small diagrams, extending previous knowledge.
Findings
Conjectural formula for gonality proposed
Proved for specific infinite families of diagrams
Confirmed for all diagrams with up to 8 dots
Abstract
A Ferrers rook graph is a graph whose vertices correspond to the dots in a Ferrers diagram, and where two vertices are adjacent if they are in the same row or the same column. We propose a conjectural formula for the gonality of Ferrers rook graphs, and prove this conjecture for a few infinite families of Ferrers diagrams. We also prove the conjecture for all Ferrers diagrams with .
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Combinatorial Mathematics · Advanced Graph Theory Research
