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Vertex-Edge Graphs
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.
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.
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.
Now that we know the
basics, let’s look at a map.
What steps will we follow
  to create a matching
   vertex-edge graph?
Step One: Identify the regions on the map.
Draw a small circle to represent a vertex in each region.
Step Two: Fill in the vertex with the
   matching color from the map.
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.
Get it?

Let’s keep practicing!
Step One: Identify the regions on the map.
Draw a small circle to represent a vertex in each region.
Step Two: Fill in the vertex with the matching color from
                          the map.
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.
You’re catching on!
 Let’s look at one
      more...
Step One: Identify the regions on the map.
Draw a small circle to represent a vertex in each region.
Step Two: Fill in the vertex with the matching color from
                          the map.
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.
To Review....
 region
                                           edge

             border



                      vertex



                      This is the vertex-edge graph
This is a map.
                       you can create from the map.
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???
The answer will soon
   be revealed....

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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....