engleski

On the calculation of the path numbers ^1Z, ^2Z and the Hosoya Z index

For acyclic molecules, Randić introduced a family of topological indices, the path numbers ^mZ, m=1,2,..., which are deduced from the Hosoya matrix. The path-number concept was recently extended to molecules containing cycles. Relations between ^1Z, ^2Z and the Hosoya index Z were established. In this work we point out several further relations for the path numbers, valid for both acyclic and cyclic systems. Using them, ^mZ can be calculated recursively, especially in the case m=1 and m=2. One of the conclusions of this study is that, from an algorithmic point of view, it is expedient to evaluate all the indices ^1Z, ^2Z,... simultaneously, and together with the Hosoya index Z.

path number ^mZ; Hosoya Z index; recursion relation

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