Valence connectivity versus Randic, Zagreb and modified Zagreb index: A linear algorithm to check discriminative properties of indices in acyclic molecular graphs

Valence connectivity in molecular graphs is described by 10-tuples mu(ij) where mu(ij) denotes the number of edges connecting vertices of valences i and j. A shorter description is provided by 4-tuples containing the number of vertices and values of Randic, Zagreb and modified Zagreb indices. Surprisingly, these two descriptions are in one-to-one correspondence for all acyclic molecules of practical interest, i.e., for all those having no more than 100 atoms. This result was achieved by developing an efficient algorithm that is linear in the number of 10-tuples