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

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12Embeddings and geometries

ARTHUR T. WHITE

1. Introduction

2. Surface models

3. Projective geometries

4. Affine geometries

5. 3-configurations

6. Partial geometries

7. Regular embeddings for PG(2, n)

8. Problems

References

        Finite geometries can be modelled by embedding associated graphs on surfaces, with vertices representing points and certain region boundaries representing lines. It is natural to seek embeddings of maximum efficiency (with largest possible Euler characteristic) and with interesting symmetries. We focus on projective and affine geometries, 3-configurations and partial geometries.

1. Introduction

Our objective in this chapter is to model finite geometries geometrically, with points and lines depicted as 0-dimensional ...

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