  Recently designed biomolecular approaches to build single chain polypeptide
polyhedra as molecular origami nanostructures have risen high interest in
various double traces of the underlying graphs of these polyhedra. Double
traces are walks that traverse every edge of the graph twice, usually with some
additional conditions on traversal direction and vertex neighborhood coverage.
Given that double trace properties are intimately related to theefficiency of
polypeptide polyhedron construction, enumerating all different possible double
traces and analyzing their properties is an important step in the construction.
In the paper, we study the automorphism group of double traces and present an
algebraic approach to this problem, yielding a branch-and-bound algorithm.
