Solving the Japanese Rope and Ring Puzzle using Graph Theory

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I was wondering if I can solve/explain the famous Japanese puzzle "Rope and Ring" with the help of Graph Theory.

If you haven't heard about it, here is the image of the puzzle:

enter image description here

We need to move the Ring from one end to other.

There are solutions in YouTube, but I am interested to view the problem from Graph-Theory point of view,

Any suggestion/help will be appreciated.