1998/01/22 by István Lukovits · 1 voice
Chemistry · Computer Science · Mathematics · #Computational Drug Discovery Methods #Graph theory and applications #Synthesis and Properties of Aromatic Compounds
paper · doi:10.1021/ci9700541
openalex publication_date 1998/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
The Wiener index W ( G ) has originally been defined for acyclic graphs. Therefore its extension to cycle-containing structures is not unambiguous; there are several possibilities, some of which have already been realized. In this paper, we proposed an “all-path” version of W and showed that its maximal value is equal to N 2 ( N − 1)2 N -4, where N denotes the number of vertices in a graph. In contrast, the maximal values of W and its close analogues, the detour index, w ( G ), and the Szeged index, Sz ( G ), are polynomials of order 4 or less in terms of N, and therefore, it may be expected that the new version will discriminate cycle-containing structures more efficiently than W ( G ), w ( G ), or Sz ( G ).