Things to know:
- Vertices have to go at crossings and at endpoints. You are also allowed
to put in extra vertices to split an edge into two edges.
- Edges go between veritices. They are squiggly and sometimes zig-zaggy lines.
Edges always start and end at vertices (though sometimes they can start and
end at the same vertex.
- Regions are the connected bits of the plane left over after you draw in
the Vertices and edges. The outside part is always a region. Don't forget
to count it.
- The Euler Characteristic (sometimes called the Euler number) is found by
calculating V-E+F. When you do this calculation for a connected
set of vertices and edges in the plane, you always get 2!
Practice problems
Count the Vertices, Faces and Edges of each of these, and then calculate the
Euler Characteristic/Euler number from the numbers you counted (verify that the Euler number is 2)
7. A. Add onto this figure in a way that will increase V and E by one each
B. Add onto this figure in a way that will increase F and E by one each
Go on to hints on the practice problems
