Fundamental Groups of Hamming Graphs
DOI:
https://doi.org/10.46787/pump.v8i.4427Keywords:
Hamming graphs; fundamental group; graph covers; discrete homotopy; graph homomorphismsAbstract
Recently there has been growing interest in discrete homotopies and homotopies of graphs beyond treating graphs as 1-dimensional simplicial spaces. One such type of homotopy is the -homotopy. Recent work by Chih-Scull has developed a homotopy category, a fundamental group for graphs under this homotopy, and a way of computing covers of graphs that lift homotopy via this fundamental group. In this paper, we compute the fundamental groups of all Hamming graphs, show that they are direct products of cyclic groups, and use this result to describe some
-homotopy covers of Hamming graphs.
Downloads
Published
2025-07-27
How to Cite
Behal, K., & Chih, T. (2025). Fundamental Groups of Hamming Graphs. The PUMP Journal of Undergraduate Research, 8, 338–358. https://doi.org/10.46787/pump.v8i.4427
Issue
Section
Articles
License
Copyright (c) 2025 Keira Behal, Tien Chih

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
The author(s) will retain the copyright, but by submitting the article agree to grant permission to the PUMP Journal of Undergraduate Research to publish, distribute, and archive the article. The author(s) will acknowledge prior publication in the PUMP Journal of Undergraduate Research for all future uses of the article or parts of it.