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~ a Graph Theory Problem

Konigsberg bridge. ~ a Graph Theory Problem. C. 6. 1. 2. Edges – (Bridges) A link joining two vertices in a graph. . A. 5. B. Vertex (vertices) - A point on a graph where one or more edges end.

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~ a Graph Theory Problem

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  1. Konigsberg bridge ~ a Graph Theory Problem C 6 1 2 Edges– (Bridges) A link joining two vertices in a graph. A 5 B Vertex(vertices) - A point on a graph where one or more edges end. Graph– A finite set of dots (vertices) and connecting links (edges). Each edge must connect two different vertices. 3 4 D 7 A graph of the bridge problem: C 6 2 1 5 B A Can you draw this graph without lifting your pencil and without redrawing an edge? 4 3 7 D

  2. Parts of a Graph Example: The graph represents cities and nonstop airline routes between them. a) How many vertices? How many edges? 5 vertices ~ the cities 7 edges ~ the nonstop airline routes between them • Path ~ a connected sequence of edges showing a route on the graph that starts at a vertex and ends at a vertex. b) Describe a path a person may travel from New York to Berlin. NLB NMRB NMRLB A ONE-WAY ticket to destination

  3. Parts of a Graph Example: The graph represents cities and nonstop airline routes between them. • Circuit ~ a path that starts and ends at the same vertex c) Describe a possible circuit that starts at Miami. MRLM A ROUND TRIP ticket returning to original city (vertex)

  4. Parts of a Graph Example: The graph represents cities and nonstop airline routes between them. • Connected ~ a graph is CONNECTED if for every pair of its vertices there is at least one PATH connecting the two vertices d) Is this graph connected? yes • Complete ~ a graph is COMPLETE of there is an edge for every pair of vertices e) Is this graph complete? no

  5. More graph theory vocabulary: Valence– the number of edges meeting at a given vertex A á 2 E á 2 B á 4 F á 4 C á 3 3 G á Is this graph connected? D á 2 2 H á Is this graph complete?

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