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

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11The genus of a group

THOMAS W. TUCKER

1. Introduction

2. Symmetric embeddings and groups acting on surfaces

3. Quotient embeddings and voltage graphs

4. Inequalities

5. Groups of low genus

6. Genera of families of groups

References

        This chapter surveys the genus of a finite group. Various symmetric embeddings of Cayley graphs are discussed, together with their associated genus parameters and their relationship to group actions on surfaces. Computations for low genus and certain families of groups are given. Particular attention is paid to general results relating the various genus parameters to each other.

1. Introduction

The (orientable) genus γ (A) of a finite group A is the smallest integer h such that some Cayley graph for A can ...

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