1. Vertex-Edge Graphs

2. The Basics
A vertex-edge graph is a graph that includes edges and vertices.
An edge is a side (shown by a straight line)
Vertices are the points where edges meet.
A map made of different regions can be represented by a vertex-edge graph.

3. There are 5 regions on this map.
The Basics
This is a MAP.
This is a
border. 1 2 5 4
This is another
border. 3
There are 5 regions on this map.

4. How many regions are on the following maps?2 2 7 3 1 1 3 6 4 4 5
There are 4 regions.
This map has 7.

5. Now that we know the basics, let’s look at a map
Now that we know the basics, let’s look at a map. What steps will we follow to create a matching vertex-edge graph?

6. Step One: Identify the regions on the map.
Draw a small circle to represent a vertex in each region.

7. Step Two: Fill in the vertex with the matching color from the map.

8. Step Three: If the regions share a border, draw a line between the two vertices. Hint- you CANNOT draw a line between two vertices that are the SAME color.

9. Get it? Let’s keep practicing!

10. Step One: Identify the regions on the map.
Draw a small circle to represent a vertex in each region.

11. Step Two: Fill in the vertex with the matching color from the map.

12. Step Three: If the regions share a border, draw a line between the two vertices. Remember- you CANNOT draw a line between two vertices that are the SAME color.

13. You’re catching on! Let’s look at one more...

14. Step One: Identify the regions on the map.
Draw a small circle to represent a vertex in each region.

15. Step Two: Fill in the vertex with the matching color from the map.

16. Step Three: If the regions share a border, draw a line between the two vertices. Remember- you CANNOT draw a line if two vertices are the SAME color.

17. To Review.... region edge border vertex This is the vertex-edge graph
you can create from the map.
This is a map.

18. What do you think? Why on earth are we studying vertex-edge
graphs? How will this type of math
help us in a real life situation???

19. The answer will soon be revealed....