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Cayley maps and symmetrical maps

Published online by Cambridge University Press:  24 October 2008

Norman Biggs
Norman Biggs
Affiliation:
Royal Holloway College, University of London
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Abstract

In this paper we shall show how combinatorial methods can be applied to the study of maps on orientable surfaces. Our main concern is with maps which possess a certain kind of symmetry, called vertex-transitivity. We show how an extension of the well-known method of Cayley can be used to construct such maps, and we give conditions which suffice for the automorphism groups of these maps to have non trivial vertex-stabilizers. Finally, we investigate the special case when the skeleton of the map is a complete graph; a classical theorem of Frobenius then implies that all vertex-transitive maps are given by our extension of Cayley's construction.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 3 , November 1972 , pp. 381 - 386
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

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