Chapter 8Drawing Graphs A: Lec 108.1 The Topology of Low Dimensions8.2 Higher-Order Surfaces8.3 Mathematical Model for Drawing Graphs

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8.1 TOPOLOGY OF LOW DIMENSIONS

Some Subsets of Eucl 2-Space and 3-Space

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Section 8.1 Topology of Low Dimensions 3

Fig 8.1.1

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Fig 8.1.2

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Section 8.1 Topology of Low Dimensions 5

Topological Equivalences of Euclidean Sets

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Figure 8.1.3

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Section 8.1 Topology of Low Dimensions 7

Fig 8.1.4

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Fig 8.1.5

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Section 8.1 Topology of Low Dimensions 9

Topological Model of a Graph

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Figure 8.1.6

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Section 8.2 Higher-Order Surfaces 11

8.2 HIGHER-ORDER SURFACES

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Torus and Möbius Band

Fig 8.2.1

Fig 8.2.2

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Section 8.2 Higher-Order Surfaces 13

Fig 8.2.3

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Fig 8.2.4

Fig 8.2.5

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Section 8.2 Higher-Order Surfaces 15

Fig 8.2.6

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Bounded and Boundaryless Surfaces

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Section 8.2 Higher-Order Surfaces 17

Closed Surfaces

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Section 8.2 Higher-Order Surfaces 19

Classification of Surfaces

Fig 8.2.7

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Fig 8.2.8

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Section 8.2 Higher-Order Surfaces 21

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8.3 MATHMODEL OF GRAPH DRAWING

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Section 8.3 Math Model of Graph Drawing 23

Figure 8.3.1

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Normalized Drawings and Imbeddings

Figure 8.3.2

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Section 8.3 Math Model of Graph Drawing 25

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Eliminating Edge-Crossings

Figure 8.3.3

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Section 8.3 Math Model of Graph Drawing 27

Fig 8.3.4

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28 Chapter 8 Drawing Graphs A: Lec 10

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Section 8.8 Supplementary Exercises 29

8.8 SUPPLEMENTARY EXERCISES

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