Planar graphs are graphs of multiple planes in which the edges do not cross.
The puzzles are of planar graphs that you need to arrange the vertices to uncross the edges of the planes.

If you like thinking-puzzle games, then you need this app in your library of games

Easy to learn but challenging to master!

Can you untangle the graph? See if you can position the vertices so that no two lines cross.
Touch and drag the circles (vertices) to rearrange the planes. A counter keeps track of the crossed edges for you. When you reach "zero" crossed edges you have solved the puzzle.
Your moves and time used are counted as well.

Highlight the non-intersecting lines for a helpful hint.

Start from the lowest vertices to get the hang of it and then move on to the the tougher levels.

This app with it's thousands of puzzles is completely free - So enjoy hours engaging play with no limitations or restrictions.
Works on phone-size screens but for optimal experience, use tablet-sized screens.