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- W1980683568 abstract "We show that if n=pe where p is an odd prime and e≥1, then the complete bipartite graph Kn,n has pe−1 regular embeddings in orientable surfaces. These maps, which are Cayley maps for cyclic and dihedral groups, have type {2n,n} and genus (n−1)(n−2)/2; one is reflexible, and the rest are chiral. The method involves groups which factorise as a product of two cyclic groups of order n. We deduce that if n is odd then Kn,n has at least n/∏p|np orientable regular embeddings, and that this lower bound is attained if and only if no two primes p and q dividing n satisfy p≡1mod(q)." @default.
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- W1980683568 date "2007-08-01" @default.
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- W1980683568 title "Regular embeddings of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math>where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si2.gif display=inline overflow=scroll><mml:mi>n</mml:mi></mml:math>is an odd prime power" @default.
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- W1980683568 doi "https://doi.org/10.1016/j.ejc.2005.07.021" @default.
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