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

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8Representing graphs and maps

TOMAŽ PISANSKI and ARJANA ŽITNIK

1. Introduction

2. Representations of graphs

3. Energy and optimal representations

4. Representations of maps

5. Representations of maps in the plane

6. Representations of incidence geometries and related topics

References

        Motivated by graph drawing problems, we can formulate a theory of graph representations precisely, admitting various generalizations. Each vertex is represented as a point in Euclidean space and each edge as a line segment spanned by the representations of its endpoints. A typical problem in this area is finding an optimal graph representation that minimizes a given energy function. For some parameters this problem admits an exact solution while other parameters ...

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