Abstract: MATH/CHEM/COMP 2002, Dubrovnik, June 24-29, 2002

Corroborating a Modification of the Wiener Index

Ivan Gutman¹ and Janez Zerovnik^2,3

¹Department of Chemistry, Faculty of Sciences, University of Kragujevac, 34000 Kragujevac, Yugoslavia

²Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, SI-2000 Maribor, Slovenia

³Department of Theoretical Computer Science, IMFM, Jadranska 19, SI-1111 Ljubljana, Slovenia

A novel modification mW of the Wiener index was put forward in a recent work of Nikolic, Trinajstic and Randic¹. 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 is any n-vertex tree, different from the n-vertex path P and the n-vertex star S, then mW(P) < mW(T) < mW(S). We also show how the concept of the modified Wiener index can be extended to weighted molecular graphs.

¹ S. Nikolic, N. Trinajstic, M. Randic, Chem. Phys. Lett. 33 (2001) 319-321.