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In this paper we examine self-dual embeddings of the complete bipartite graph K", on both orientable and nonorientable surfaces. It can be quickly established that such an embedding can exist only if both n and m are even integers exceeding 2. We show by construction that these necessary conditions are sufficient, except that there is no orientable self-dual embedding of K6,6. 0doi:10.1016/0095-8956(92)90056-4 fatcat:6mnkxinrejhgrcc3gys4z3ja64