vertex-edge graphs. the basics ❖ a vertex-edge graph is a graph that includes edges and vertices....
TRANSCRIPT
![Page 1: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/1.jpg)
Vertex-Edge Graphs
![Page 2: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/2.jpg)
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.
![Page 3: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/3.jpg)
The BasicsThis is a MAP.
There are 5 regions on this map.
1
2
3
45
This is a border.
This is anotherborder.
![Page 4: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/4.jpg)
How many regions are on the following maps?
1
2
3
4
1
23
45
6
7
There are 4 regions. This map has 7.
![Page 5: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/5.jpg)
Now that we know the basics, let’s look
at a map. What steps will we follow to
create a matching vertex-edge graph?
![Page 6: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/6.jpg)
Step One: Identify the regions on the map.Draw a small circle to represent a vertex in
each region.
![Page 7: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/7.jpg)
Step Two: Fill in the vertex with the matching color from the map.
![Page 8: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/8.jpg)
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.
![Page 9: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/9.jpg)
Get it?
Let’s keep practicing!
![Page 10: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/10.jpg)
Step One: Identify the regions on the map.Draw a small circle to represent a vertex in
each region.
![Page 11: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/11.jpg)
Step Two: Fill in the vertex with the matching color from the map.
![Page 12: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/12.jpg)
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.
![Page 13: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/13.jpg)
You’re catching on!Let’s look at one
more...
![Page 14: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/14.jpg)
Step One: Identify the regions on the map.Draw a small circle to represent a vertex in
each region.
![Page 15: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/15.jpg)
Step Two: Fill in the vertex with the matching color from the map.
![Page 16: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/16.jpg)
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.
![Page 17: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/17.jpg)
To Review....
This is a map.This is the vertex-edge graphyou can create from the map.
vertex
edgeregion
border
![Page 18: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/18.jpg)
What do you think?
Why on earth are we studying vertex-edgegraphs? How will this
type of mathhelp us in a real life
situation???
![Page 19: Vertex-Edge Graphs. The Basics ❖ A vertex-edge graph is a graph that includes edges and vertices. ❖A❖An edge is a side (shown by a straight line) ❖ V❖](https://reader036.vdocuments.us/reader036/viewer/2022062417/551bdccc550346be588b5b8a/html5/thumbnails/19.jpg)
The answer will soon be
revealed....