Determine valid source-vertex covers for Scenario 3 pots

Determine which vertex covers of a graph can be used as source vertices in a valid Scenario 3 pot in the flexible tile model for DNA self-assembly.

Background

The paper constructs Scenario 3 pots by selecting a vertex cover K and assigning distinct bond-edge types to its source vertices. Edges within the cover require an additional orientation choice, and not every vertex cover yields a valid pot: the cube graph example shows that a minimum vertex cover can produce a pot realizing a nonisomorphic graph of the same order. The unresolved issue is therefore to characterize precisely which vertex covers, possibly together with suitable orientations, prevent the formation of forbidden outputs.