ON THE CALCULATION OF THE PATH NUMBERS (1)Z, (2)Z AND THE HOSOYA Z-INDEX

For acyclic molecules, Randic(4) introduced a family of topological in dices, the path numbers (m)Z, m = 1, 2,..., which are deduced from the Hosoya matrix. The path-number concept was recently extended to molec ules containing cycles. Relations between (1)Z, (2)Z and the Hosoya in dex Z were established.(6) In this work we point out several further r elations for the path numbers, valid for both acyclic and cyclic syste ms. Using them, (m)Z can be calculated recursively, especially in the case m = 1 and m = 2. One of the conclusions of this study is that, fr om an algorithmic point of view, it is expedient to evaluate all the i ndices (1)Z, (2)Z,... simultaneously, and together with the Hosoya ind ex Z.