Original scientific paper

On the Calculation of the Path Numbers 1Z, 2Z and the Hosoya Z Index

Ivan Gutman ; Institute for Advanced Studies, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
Dejan Plavšić ; The Ruder Bošković Institute, P.O.B. 1016, HR-10001 Zagreb, The Republic of Croatia
Milan Šoškić ; Department of Chemistry, Faculty of Agriculture, University of Zagreb, HR-10000 Zagreb, The Republic of Croatia
Irena Landeka ; Department of Biochemistry, Faculty of Science, University of Zagreb, HR-10000 Zagreb, The Republic of Croatia
Ante Graovac ; The Ruder Bošković Institute, P.O.B. 1016, HR-10001 Zagreb, The Republic of Croatia

Abstract

For acyclic molecules, Ranđić4 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 lZ, 2Z and the Hosoya index Z were established.6 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.

Keywords

Hrčak ID:

135664

URI

https://hrcak.srce.hr/135664

Publication date:

3.11.1997.

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