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Ch. 9: Graph Theory

Ch. 9: Graph Theory. 9.1 Intro to Graphs. Uses. Degree of separation- Hollywood, acquaintance , collaborate- Erdos Travel between cities Konigsberg bridge Shortest path Least cost Schedule exams, assign channels, rooms Number of colors on a map

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Ch. 9: Graph Theory

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  1. Ch. 9: Graph Theory 9.1 Intro to Graphs

  2. Uses • Degree of separation- Hollywood, acquaintance, collaborate-Erdos • Travel between cities • Konigsberg bridge • Shortest path • Least cost • Schedule exams, assign channels, rooms • Number of colors on a map • Highway inspecting, snow removal, street sweeping • Mail delivery • Niche overlap- ecology • Influence graphs • Round-robin tournaments • Precedence graphs

  3. G=(V,E) G=(V,E) where V is the set of vertices and E is the set of edges Terminology is not standard from book to book. Types of Graphs – see handout Simple G=(V,E) where E is the set of unordered pairs Multigraph Pseudo-graph Directed Graph G=(V,E) where E is the set of ordered pairs of edges Directed Multigraph

  4. Simple and multigraph • Simple graph G=(V,E) where E is the set of unordered pairs • Multigraph

  5. Pseudo and directed graphs • Pseudo-graph • Directed Graph G=(V,E) where E is the set of ordered pairs of edges

  6. multigraph • Directed Multigraph

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