In each puzzle, fill the circles with the numbers 1, 2, 3, ... n, where n is the number of circles in such a way that consecutive numbers are NOT in circles that are joined with a line.
Here are the solutions:
In each of the puzzles, there's a special circle (highlighted in yellow below):
Each yellow circle has a special property - it connects to all other circles but one, the one marked in orange. This means it can't be in the middle of the sequence - it must be at one of the two ends. The symmetric counterparts of the yellow circles also have this property. This lets you place numbers 1, 2, $n$, and $n-1$ immediately; the rest of the circles are easy to fill.