Atomic Molecular Distance Code and Index

Randic introduced 53) the so-called atomic and molecular path codes in an attempt to characterize uniquely molecular structures. The atomic (or vertex) path code of the atom j, VPC(j), represents the power series  

The molecular (or graph) path code, GPC(G), is obtained similarly by summation over all atoms (vertices) in the molecule (graph G)  

More frequently, the two codes are used in linear form  

Though these codes failed to characterize uniquely the molecular structure54), they are useful for ordering structures as basis for systematic searches for regularities in molecular data 55), fragment56) and ring S7) search, for recognition of structural similarity 54 in molecules, for the prediction of chemical shift in NMR-data, etc. 

For polycyclic structures it seems reasonable to introduce 59) vertex and graph distance codes, VDC and GDC, instead of path codes  

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