Classification of nonorientable regular embeddings of Hamming graphs

Details Classification of nonorientable regular embeddings of Hamming graphs Classification of nonorientable regular embeddings of Hamming graphs

2011-07-16

arxiv.org/abs/1107.3187v1

Mathematics

Combinatorics

13 pages

Scientific paper

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.

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