I'm imposing a further restraint that we want want vertex to be labeled 0, and the highest labeled 7.
So two are 0,7 we could guess they could be 0,1,2,3,7. With these numbers every natural number difference up to 7 is possible.
We could brute force the solution by trying every possibility but this goes up with factorial complexity so I found a way to solve them directly.
Consider the following system of equations and the solution (which Maple found in a fraction of a second)
The first one is: