Directed Graphs
AZ Standard 2.4.1
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?
Edge
Node or Vertex
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 roundrobin 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.
Fees
Gililland
Connolly
McKemy
Draw & label four nodes to
represent the teams.
Make a Directed Graph
Fees
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.
Gililland
Connolly
McKemy
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.
Fees
Gililland
Connolly
McKemy
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.
Fees
Gililland
Connolly
McKemy
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.
Fees
Gililland
Connolly
McKemy
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
Fees
Gililland
Connolly
McKemy
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
Answers:
A - B - C; B - C - A;
C-A-B
C