A review is presented of the recent progress in designing local vertex
invariants with low intramolecular degeneracy and the derived topolog
ical indices with low intermolecular degeneracy, in other words, an at
tempt is made to assign to graph vertices real (i.e, non-integer) nume
rical invariants which are different for non-equivalent vertices and s
imilarly to assign to non-isomorphic molecular graphs distinct real-nu
mber topological indices.