20. There is a pentagon $A B C D E$. If the vertices $A$, $B$, $C$, $D$, $E$ are colored with one of the three colors: red, yellow, green, such that adjacent vertices are colored differently, then there are a total of different coloring methods.
20.30.

If point $A$ is colored red (as shown in Figure 11), there are 10 coloring methods.
Figure 11

Similarly, if point $A$ is colored yellow or green, there are also 10 coloring methods each. Therefore, there are a total of 30 different coloring methods.