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Exploring Graph Theory: Applications and Fundamental Concepts

This comprehensive introduction to graph theory covers fundamental concepts and diverse applications. Learn about the degree of separation in networks like Hollywood, the significance of the Konigsberg bridge, and the strategies for finding the shortest path and least cost solutions in various contexts. Explore practical uses, such as scheduling exams, optimizing mail delivery, and managing resources like highway inspections. The discussion includes types of graphs, including simple, multigraphs, directed graphs, and more, highlighting their relevance in real-world problems.

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Exploring Graph Theory: Applications and Fundamental Concepts

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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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