This may be the wrong forum, as it's sort of about programming also.
I'm trying to encode a directed Hamiltonian cycle for a standard set of 28 6-dominos. The difficulty I am having is trying to keep the path directed, but dominoes can be rotated, and once a domino is used as an endpoint, the next node has to be connected by its other value. For instance, 2:3 connects to 3:4 via the shared 3, so the 3:4 tails are connected by the 4. But if the 4 of the 3:4 domino is used as a tail, then it's own tails are now connected to the 3.
I need to find an encoding for the dominoes which tabulates each head followed by it's tails, this is to be used as a partial constraint in a satisfiability problem.
I've thought about it some more, and I'm wondering if this would be a (part!) solution? - It would mean encoding each domino as two nodes...
I must be missing something, because I see chains such as ..(3, 1)-(1, 4)-(4, 0)-(0, 6)-(6, 1)-(1, 3)-(3, 2)-(2, 5), and the mirror/rotation of a domino is itself!
Update
So the following structure seems to work, but it required me to use an external constraint on the Hamiltonian to restrict access to just one of the two mirrored nodes. If there is a means of being able to defined the nodes and arcs such that the constraint can happen within the definition of the circuit.
It's recreational, and I am the first to admit I am out of my depth, so please be kind.