Original scientific paper

Corroborating a Modification of the Wiener Index

Ivan Gutman ; Faculty of Science, University of Kragujevac, 34000 Kragujevac, Yugoslavia
Janez Žerovnik ; Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, 2000 Maribor; Slovenia

Abstract

In a recent work [Chem. Phys. Lett. 333 (2001) 319-321] Nikolić, Trinajstić, and Randić put forward a novel modification mW of the Wiener index. We now show that mW possesses the basic properties required by a topological index to be acceptable as a measure of the extent of branching of the carbon-atom skeleton of the respective molecule (and therefore to be a structure-descriptor, potentially applicable in QSPR and QSAR studies). In particular, if T_n is any n-vertex tree, different from the n-vertex path P_n and the n-vertex star S_n, then mW(P_n) < mW(T_n) < mW(S_n). We also show how the concept of the modified Wiener index can be extended to weighted molecular graphs.

Keywords

Wiener index; modified Wiener index; weighted modified Wiener index; branching; Chemical graph theory

Hrčak ID:

127539

URI

https://hrcak.srce.hr/127539

Publication date:

3.6.2002.

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