[fgbwjvbx] Graphs with large edit distance

Start with a graph.  Select some subset of the subgraphs of the graph that have a large Hamming distance (adding or deleting edges from the original graph) between them, like bits in coding theory.  Let these be letters in an invented alphabet whose letters are less likely to be confused for each other even if letters get damaged.

Restrict to Hamiltonian subgraphs, drawable in one stroke.

The starting graph could be a 7-segment display.