Petersen Eight Graph Sum Puzzle

Generalized Petersen Graphs have some very nice mathematical properties and also make for a very nice place to design puzzles.  In this puzzle I'm using the graph GP(8,3) which is also known as the Möbius–Kantor graph.  None of that knowledge is necessary to solve this puzzle.

The rules are simple.  Enter the numbers 1 through 8 into the large circular cells so that each number appears twice  and no two adjacent cells have the same number.  The clues on the edges between cells reveal the sum of those two cells.  A numberless clue indicates that the sum is larger than eight without revealing what that sum is.  

The solution and a PDF version can be found below.



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