Classification of nonorientable regular embeddings of Hamming graphs

2011/07/16 by Gareth A. Jones, Jones, Gareth A., Young Soo Kwon +1
Computer Science · Mathematics · #05C10 #05C30 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #math.CO #msc:05C10 #msc:05C30

paper · pdf · doi:10.48550/arxiv.1107.3187

13 pages

arxiv created 2011/07/16 · openalex publication_date 2011/07/16 · arxiv updated 2011/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By a regular embedding of a graph K in a surface we mean a 2-cell embedding of K in a compact connected surface such that the automorphism group acts regularly on flags. In this paper, we classify the nonorientable regular embeddings of the Hamming graph H(d,n). We show that there exists such an embedding if and only if n=2 and d=2, or n=3 or 4 and d>0, or n=6 and d=1 or 2. We also give constructions and descriptions of these embeddings.

Citations

• Classification and Galois conjugacy of Hamming maps

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