  Coarse grain (CG) molecular dynamics (MD) can simulate systems inaccessible
to fine grain (FG) MD simulations. A CG simulation decreases the degrees of
freedom by mapping atoms from an FG representation into agglomerate CG
particles. The FG to CG mapping is not unique. Research into systematic
selection of these mappings is challenging due to their combinatorial growth
with respect to the number of atoms in a molecule. Here we present a method of
reducing the total count of mappings by imposing molecular topology and
symmetry constraints. The count reduction is illustrated by considering all
mappings for nearly 49,889 molecules. The resulting number of mapping operators
is still large, so we introduce hierarchical graphs which encode multiple CG
mapping operators. The encoding method is demonstrated for methanol and a
14-mer peptide. This encoding provides a foundation to perform automated
mapping selection.
