Degeneracy of Topologic Distance Descriptors for Cubic Molecular Graphs:  Examples of Small Fullerenes

The degeneracy of topological distance sum (DS) and distance degree sequence (DDS) of small fullerenes is analyzed. The degeneracy of the two topological descriptors is determined by comparing the topological equivalence classes of the fullerene atoms with the DS and DDS classes, respectively. On the basis of DS and DDS degenerated fullerene graphs and by using two previously demonstrated theorems it is possible to generate pairs of graphs with degenerated topological indices based on DS (e.g., W, J) and on DDS (e.g., U, V, X, Y).