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Topics in Topological Graph Theory by Jonathan L. Gross, Robin J. Wilson, Lowell W. Beineke

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10Symmetric maps

JOZEF ŠIRÁimages and THOMAS W. TUCKER

1. Introduction

2. Representations of maps

3. Regular maps

4. Cayley maps

5. Regular Cayley maps

6. Edge-transitive maps

7. Maps and mathematics

References

        A map is a graph embedding in which the focus is on the vertex-edge-face incidence relation together with its morphisms. This chapter concentrates on maps that are highly symmetric: regular maps, Cayley maps, regular Cayley maps and edge-transitive maps. In each case, we show how to construct a map using only information about the automorphism group. As a consequence, the viewpoint and methods are almost entirely group-theoretic.

1. Introduction ...

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