Abstract: MATH/CHEM/COMP 2002, Dubrovnik,
June 2429, 2002

Corroborating a
Modification of the Wiener Index
Ivan Gutman^{1} and Janez Zerovnik^{2,3} ^{1}Department of
Chemistry, Faculty of Sciences, University of Kragujevac, 34000 Kragujevac, Yugoslavia ^{2}Faculty of
Mechanical Engineering, University of Maribor, Smetanova 17, SI2000 Maribor,
Slovenia
A novel modification mW of the Wiener index was put forward in a recent work of Nikolic, Trinajstic and Randic^{1}. 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 carbonatom skeleton of the respective molecule (and therefore to be a structuredescriptor, potentially applicable in QSPR and QSAR studies). In particular, if T is any nvertex tree, different from the nvertex path P and the nvertex 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) 319321. 