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- W1978435515 abstract "In this paper the classification of the edge-symmetric imbeddings of the complete graphs K n in orientable surfaces is completed. Biggs showed that regular imbeddings of complete graphs in oriented surfaces exist iff n is a prime power p ie , his examples being Cayley maps based on the finite field F = GF ( n ). It has since been shown [5] that these are the only examples, and that there are φ ( n - 1)/ e isomorphism classes of such maps (where φ is Euler's function), each corresponding to a conjugacy class of primitive elements of F . We show that non-regular edge-symmetric imbeddings of complete graphs in oriented surfaces exist iff n is a prime power p e greater than 3 and congruent to 3 mod 4, that they too are Cayley maps based on the finite field F = GF ( n ), and that there arc 1/4( n - 3) φ ( n - 1)/ e isomorphism classes of such maps." @default.
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- W1978435515 date "1990-03-01" @default.
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- W1978435515 title "Edge-symmetric Orientable Imbeddings of Complete Graphs" @default.
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- W1978435515 doi "https://doi.org/10.1016/s0195-6698(13)80067-4" @default.
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