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 Highway inspecting, snow removal, street sweeping Mail delivery Niche overlap- ecology Influence graphs Round-robin tournaments Precedence graphs

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

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

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

multigraph Directed Multigraph