Cayley Graphs

Cayley graphs describe adjacency through a group and a choice of generators. My work uses this algebraic structure to study graph coloring, from circulants to monomial Cayley graphs arising in the Hadwiger–Nelson problem.

Papers

• Coloring Monomial Cayley Graphs: The One-Parameter Case
• Chromatic numbers of circulants with indispensable generators

Planned Background Articles

• Cayley and Circulant Graphs — Groups, generating sets, and the effect of generators on chromatic number, providing background for the circulants paper.
• Unit-Distance Graph Coloring — The Hadwiger–Nelson problem, finite witnesses, and the role of geometric configurations in proving coloring bounds.
• Monomial Cayley Graphs — The algebraic construction behind my paper and how finite configurations and computational searches help reveal its coloring properties.

For a visual example from the monomial Cayley graphs paper, explore the finite witness simulation.