Representations of graphs

author:Tomaž Pisanski, IMFM
published: Feb. 25, 2007, recorded: November 2005, views: 304

Slides

Slides
0:10	Representation of graphs (Tutorial)
0:16	Representations A personal history
3:56	Examples
4:01	Representation of Graphs
5:38	Representation of Graphs
6:11	Graph Representation Examples
7:18	Edge Representation
8:14	Edge Extensions
8:48	One Dimensional Real Representation
9:34	Local Search
9:44	r-Neighborhoods
9:48	Neighborhoods in Graphs
9:52	Local Search Algorithm
9:55	Simulated Annealing - Idea
10:00	One Dimensional Representations and Nodal Domains
11:50	Characteristic Vector
12:38	Vertex Coloring as Graph Representation
13:38	Identity Representation
13:43	Point Configuration
14:45	Graph Construction from Point Configurations
15:30	slide22
16:05	Flat Torus
16:07	Flat Torus
16:43	Embeddings are Representations
17:23	New Representations from Old
18:39	Stereographic Projection
18:42	Stereographic projection and representations
18:42	Example
19:08	Example
19:30	Representation of Graphs in Metric Space
20:33	Euclidean metric in Rn.
20:45	Metric Space - Revisited
20:51	Three Classical Results
22:52	The Energy
22:56	Some Energy Models
23:00	Tutte’s Planarity Algorithm
24:14	Tutte’s Embedding
24:45	Edge-repulsion LinLog Model
26:09	The Laplace Representation
27:02	Nodal Domains - Revisited
27:57	Congruence and Similarity
28:00	Similar Representations
28:02	Unit Distance Graphs
29:26	Generalized Petersen Graphs
29:58	Symmetry of Representation
30:01	Representations with Symmetry (Motivation: Recent work on regular polygons and regular polyhedra by Branko Grünbaum)
30:02	An Example
30:04	A General Problem

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Description

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 graph visualization has been developed under the name of "graph representations". In this tutorial we present an outline of the theory of graph representations.