Fundamental Groups of Hamming Graphs

Authors

  • Keira Behal Emory University
  • Tien Chih Emory University

DOI:

https://doi.org/10.46787/pump.v8i.4427

Keywords:

Hamming graphs; fundamental group; graph covers; discrete homotopy; graph homomorphisms

Abstract

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 {\displaystyle \times }-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 {\displaystyle \times }-homotopy covers of Hamming graphs.

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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