ON THE BASIS OF INVARIANTS OF LABELED MOLECULAR GRAPHS

It is proved that any molecular graph invariant (that is any topologic al index) can be uniquely represented as (1) a linear combination of o ccurrence numbers of some substructures (fragments), both connected an d disconnected, or (2) a polynomial on occurrence numbers of connected substructures of corresponding molecular graph. Besides, any (0,1)-va lued molecular graph invariant can be uniquely represented as a linear combination (in the terms of logic operations) of some basic (0,1)-va lued invariants indicating the presence of some substructures in the c hemical structure. Thus, the occurrence numbers of substructures in a structure (or numbers indicating the presence or absence of substructu res in a structure for the case of (0,1)-valued invariants) are shown to constitute the basis of invariants of labeled molecular graphs. A p ossibility to use these results for the mathematical justification of substructures-based methods in the ''structure-property'' problem is a lso discussed.