Directed Graphs AZ Standard 2.4.1 Use directed graphs to solve problems.

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Presentation transcript:

Directed Graphs AZ Standard Use directed graphs to solve problems.

What is a directed graph?  A graph whose edges have directions.  Arrows on the edges give directional information.  In the example to the right you can move from A to B but not B to A.  Can you name two other allowed moves? Node or Vertex Edge

Why do we use directed graphs?  We use this type of graph to help represent problems and then solve them.  For example: UPS needs to establish the most efficient delivery routes possible.  Why would they want to do this?

Using Directed Graphs to Solve Problems Connolly’s softball team is playing in a round- robin tournament, where every TD3 middle school plays every other school.Given the information on the next slide, rank the teams from 1st to last place.

Using Directed Graphs to Solve Problems Fees beats Connolly and McKemy, Connolly beats Gililland, McKemy beats Connolly and Gililland, And Gililland beats Fees. Rank the teams from 1st to last place. Next slide- how to make a directed graph to solve this problem.

Make a Directed Graph Fees beats Connolly and McKemy, Connolly beats Gililland, McKemy beats Connolly and Gililland, And Gililland beats Fees. Rank the teams from 1st to last place. FeesConnolly GilillandMcKemy Draw & label four nodes to represent the teams.

Make a Directed Graph Fees beats Connolly and McKemy, Connolly beats Gililland, McKemy beats Connolly and Gililland, And Gililland beats Fees. Rank the teams from 1st to last place. Draw lines & arrows between teams that played games. Arrows point to losing team. FeesConnolly GilillandMcKemy

Make a Directed Graph Fees beats Connolly and McKemy, Connolly beats Gililland, McKemy beats Connolly and Gililland, And Gililland beats Fees. Rank the teams from 1st to last place. FeesConnolly GilillandMcKemy Draw lines & arrows between teams that played games. Arrows point to losing team.

Make a Directed Graph Fees beats Connolly and McKemy, Connolly beats Gililland, McKemy beats Connolly and Gililland, And Gililland beats Fees. Rank the teams from 1st to last place. FeesConnolly GilillandMcKemy Draw lines & arrows between teams that played games. Arrows point to losing team.

Make a Directed Graph Fees beats Connolly and McKemy, Connolly beats Gililland, McKemy beats Connolly and Gililland, And Gililland beats Fees. Rank the teams from 1st to last place. FeesConnolly GilillandMcKemy Draw lines & arrows between teams that played games. Arrows point to losing team.

Make a Directed Graph Rank the teams from 1st to last place. -notice that each team played 3 games (count lines leaving each vertex) -Fees - 2 wins -Connollly - 1 win -Gilliland - 1 win -McKemy - 2 wins FeesConnolly GilillandMcKemy Fees & McKemy must play 1 more game to decide winner.

Directed Graph and Hamilton Paths  A Hamilton Path travels from vertex (node) to vertex (node) JUST ONCE.  List all Hamilton Paths in the directed graph on this slide. A B C

Directed Graph and Hamilton Paths  A Hamilton Path travels from vertex (node) to vertex (node) JUST ONCE.  List all Hamilton Paths in the directed graph on this slide. A B C Answers: A - B - C; B - C - A; C - A - B