What's the general rule for constructing such graphs? I mean actually drawing it on paper.
Start with the 1-cube, two points: and label them A and B. Now create 2 copies of the 1-cube and place A's and B's before each points label on the top and bottom copies, respectfully. Like this:
Also connect the points that have the same label other than the first letter (dashed-line in pic). And so on... Color the graph according to the first letter (or last).
Separate names with a comma.