Corroborating a modification of the Wiener index
İvan Gutman, Janez Žerovnik · University of Maribor digital library (University of Maribor) · 2002
In a recent work [Chem.Phys.Lett.333 (2001) 319-321] Nikoli}, Trinajsti}, and Randi} put forward a novel modification m W of the Wiener index.We now show that m W 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 m W(P n ) < m W(T n ) < m W(S n ).We also show how the concept of the modified Wiener index can be extended to weighted molecular graphs.