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Vertex-Edge Graphs

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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.

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**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.

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**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.

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**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?

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**Step One: Identify the regions on the map. **

Draw a small circle to represent a vertex in each region.

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

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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.

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**Get it? Let’s keep practicing!**

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**Step One: Identify the regions on the map. **

Draw a small circle to represent a vertex in each region.

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

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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.

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

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**Step One: Identify the regions on the map. **

Draw a small circle to represent a vertex in each region.

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

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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.

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**To Review.... region edge border vertex This is the vertex-edge graph**

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

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**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???

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**The answer will soon be revealed....**

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