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.

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.

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