Automorphisms of imbedded graphs |
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Authors: | Norman Biggs |
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Affiliation: | Royal Holloway College, University of London, England |
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Abstract: | If a linear graph is imbedded in a surface to form a map, then the map has a group of automorphisms which is a subgroup (usually, a proper subgroup) of the automorphism group of the graph. In this note it will be shown that, for any imbedding of Kn in an orientable surface, the order of the automorphism group of the resulting map is a divisor of n(n − 1), and that the order equals n(n − 1) if and only if n is a prime power. The explicit construction of imbeddings of KQ, q = pm with map automorphism group of order q(q − 1) gives rise to new types of regular map. There are also tenous connections with the theory of Frobenius groups. |
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