Abstract
The path numbers of the mth order, mZ, of a connected undirected graph are introduced and studied analitically. The definition of the 1Z and 2Z indices for acyclic graphs proposed earlier is generalized in order to cover cyclic graphs. The relationships between the path numbers 1Z and 2Z and the Hosoya Z index are discussed. It is shown that the path number 1Z and the Hosoya Z index are closely related graph-theoretical invariants. The information contents of the 1Z and 2Z indices are only slightly overlapped, and hence the indices could be used as “independent” predictor variables in structure−property−activity studies.
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