- A vertex-edge graph is a graph that represents relationships between points (vertices) and connections between them (edges). - Vertices are represented by circles or points, and edges are straight lines that connect vertices. - Maps can be represented as vertex-edge graphs, with each region of the map as a vertex and borders between regions as edges. - The document provides steps to take a map and create a matching vertex-edge graph representation, including identifying regions, drawing vertices, and connecting vertices with edges between regions that share borders.

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. 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.
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
This is a map.
you can create from the 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....