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SECTION 5.1: Euler Circuit Problems

SECTION 5.1: Euler Circuit Problems . What is a routing problem?. Routing problems deal with finding ways to deliver goods and/or services to many different destinations. Does a possible route exist or which one of the possible routes is the most efficient?

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SECTION 5.1: Euler Circuit Problems

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  1. SECTION 5.1: Euler Circuit Problems

  2. What is a routing problem? • Routing problems deal with finding ways to deliver goods and/or services to many different destinations. Does a possible route exist or which one of the possible routes is the most efficient? • Examples of routing problems: delivering mail, walking through a neighborhood…

  3. The Seven Bridges of Konigsberg: A prize is offered to the first person who can find a way to walk across each one of the seven bridges of Konigsberg without re-crossing any and return to the original starting point. bridge

  4. SECTION 5.2: GRAPHS

  5. A graph is a picture consisting of vertices (dots) and edges (lines). The edges do not have to be straight lines but they have to connect two vertices. • Example: or

  6. A loop is an edge connecting a vertex back with itself. This is a loop named BB No loop

  7. An isolated vertex is the vertex that is not connected to any other vertex. Vertex F is an isolated vertex

  8. Multiple edges have two vertices for which there exists more than one edge connecting them. These are multiple edges CD or DC

  9. Disconnected graph: a graph made up of connected pieces • Example: • Components - pieces of disconnected graphs which are themselves connected G

  10. List vertex set and edge set • Vertex set V = • Edge set E =

  11. Example • Consider the graph with V={A, B, C, D, E} and E={AC, AE, BD, BE, CA, CD, CE, DE} Draw several different pictures of the graph.

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