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.
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.
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???