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Representations of graphs
Published on Feb 25, 20077170 Views
A graph is a mathematical structure that is sometimes hard to separate from its visualization. An important branch of graph theory studies graph drawing problems. Recently a mathematical approach to g
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Chapter list
Representation of graphs (Tutorial)00:10
Representations A personal history00:16
Examples03:56
Representation of Graphs04:01
Representation of Graphs05:38
Graph Representation Examples06:11
Edge Representation07:18
Edge Extensions08:14
One Dimensional Real Representation08:48
Local Search09:34
r-Neighborhoods09:44
Neighborhoods in Graphs09:48
Local Search Algorithm09:52
Simulated Annealing - Idea09:55
One Dimensional Representations and Nodal Domains10:00
Characteristic Vector11:50
Vertex Coloring as Graph Representation12:38
Identity Representation13:38
Point Configuration13:43
Graph Construction from Point Configurations14:45
slide2215:30
Flat Torus16:05
Flat Torus16:07
Embeddings are Representations16:43
New Representations from Old17:23
Stereographic Projection18:39
Stereographic projection and representations18:42
Example18:42
Example19:08
Representation of Graphs in Metric Space19:30
Euclidean metric in Rn.20:33
Metric Space - Revisited20:45
Three Classical Results 20:51
The Energy22:52
Some Energy Models22:56
Tutte’s Planarity Algorithm23:00
Tutte’s Embedding24:14
Edge-repulsion LinLog Model24:45
The Laplace Representation26:09
Nodal Domains - Revisited27:02
Congruence and Similarity27:57
Similar Representations28:00
Unit Distance Graphs28:02
Generalized Petersen Graphs29:26
Symmetry of Representation29:58
Representations with Symmetry (Motivation: Recent work on regular polygons and regular polyhedra by Branko Grünbaum) 30:01
An Example30:02
A General Problem30:04