The limits of a recently proposed computer method for finding all distinct substructures of a chemical structure
are systematically explored within comprehensive graph samples which serve as supersets of the graphs
corresponding to saturated hydrocarbons, both acyclic (up to n ) 20) and (poly)cyclic (up to n ) 10).
Several pairs of smallest graphs and compounds are identified that cannot be distinguished using selected
combinations of invariants such as combinations of Balaban’s index J and graph matrix eigenvalues. As the
most important result, it can now be stated that the computer program NIMSG, using J and distance
eigenvalues, is safe within the domain of mono- through tetracyclic saturated hydrocarbon substructures up
to n ) 10 (oligocyclic decanes) and of all acyclic alkane substructures up to n ) 19 (nonadecanes), i.e., it
will not miss any of these substructures. For the regions surrounding this safe domain, upper limits are
found for the numbers of substructures that may be lost in the worst case, and these are low. This taken
together means that the computer program can be reasonably employed in chemistry whenever one is interested
in finding the saturated hydrocarbon substructures. As to unsaturated and heteroatom containing substructures,
there are reasons to conjecture that the method’s resolving power for them is similar.