On the identification numbers for chemical structures

Several identification (ID) numbers for chemical structures (connectivity ID number, prime ID number, weighted ID number) are analyzed and tested until a counterexample (a pair of structures with the same ID number) is found. The analysis is carried out for acyclic structures with up to 20 atoms, trees with up to 20 points, benzenoid graphs and polyhexes with up to 10 hexagons, and all connected graphs with up to 6 points. Although all the (chemical) ID numbers studied are highly selective for many families of (molecular) graphs, none of them are unique: in all three cases the counterexamples are found. However, the greatest discriminative power is shown by the weighted ID number.