Abstract: MATH/CHEM/COMP 2002, Dubrovnik, June 24-29, 2002
Corroborating a Modification of the Wiener Index
Ivan Gutman1 and Janez Zerovnik2,3
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
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.