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

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9Enumerating coverings

JIN HO KWAK and JAEUN LEE

1. Introduction

2. Graph coverings

3. Regular coverings

4. Surface branched coverings

5. Regular surface branched coverings

6. Distribution of surface branched coverings

7. Further remarks

References

        Many graphs with a symmetry property can be described as coverings of simpler graphs. In this chapter, we survey several enumeration problems for various types of non-isomorphic graph coverings of a graph and of surface branched coverings. We also discuss the distribution of surface branched (regular) coverings of a surface through the genera of supporting surfaces.

1. Introduction

Consider the map from the 3-dimensional cube Q3 to the complete graph K4, defined by identifying antipodal points ...

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