Cantankerous maps and rotary embeddings of Kn
Journal of Combinatorial Theory Series B
Regular embeddings of Kn,n where n is a power of 2. I: Metacyclic case
European Journal of Combinatorics
Regular embeddings of Kn,n where n is an odd prime power
European Journal of Combinatorics
Complete bipartite graphs with a unique regular embedding
Journal of Combinatorial Theory Series B
Regular orientable embeddings of complete bipartite graphs
Journal of Graph Theory
Classification of regular embeddings of n-dimensional cubes
Journal of Algebraic Combinatorics: An International Journal
On the orientable regular embeddings of complete multipartite graphs
European Journal of Combinatorics
Classification of nonorientable regular embeddings of Hamming graphs
European Journal of Combinatorics
A classification of orientably-regular embeddings of complete multipartite graphs
European Journal of Combinatorics
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A 2-cell embedding of a graph G into a closed (orientable or nonorientable) surface is called regular if its automorphism group acts regularly on the flags - mutually incident vertex-edge-face triples. In this paper, we classify the regular embeddings of complete bipartite graphs K"n","n into nonorientable surfaces. Such a regular embedding of K"n","n exists only when n is of the form n=2p"1^a^"^1p"2^a^"^2...p"k^a^"^k where the p"i are primes congruent to +/-1 mod 8. In this case, up to isomorphism the number of those regular embeddings of K"n","n is 2^k.