Classification of reflexible regular embeddings and self-Petrie dual regular embeddings of complete bipartite graphs Original Research Article

In this paper, we classify the reflexible regular orientable embeddings and the self-Petrie dual regular orientable embeddings of complete bipartite graphs. The classification shows that for any natural number n, say image image are distinct odd primes and image for each image, there are t distinct reflexible regular embeddings of the complete bipartite graph image up to isomorphism, where image if image, image if image, image if image, and image if image. And, there are s distinct self-Petrie dual regular embeddings of image up to isomorphism, where image if image, image if image, image if image, and image if image.