Atomic subspaces of {L_1}-martingale spaces

In Part I of the present paper the following problem was investigated. Let G be a finite simple graph, and S be a finite set of primes. We say that G is representable with S if it is possible to attach rational numbers to the vertices of G such that the vertices v₁, v₂ are connected by an edge if and only if the difference of the attached values is an S-unit. In Part I we gave several results concerning the representability of graphs in the above sense.