ABSTRACT
Wiener index (W) belongs to the set of graph invariants, and it is remembered as the first molecular-graph descriptor applied in 1947 to investigate the correlations between physicochemical properties and the topological structure of the organic compounds. The visionary assumption originally made by Wiener consisted in describing an organic molecule just like a graph, a simple mathematical object made by two sole elements, vertices (the carbon atoms) and edges (the molecular bonds). W was the first distance-based topological descriptor appeared on the theoretical chemistry scene. Outstanding applications of W in the nanosystems field concern defective graphenic layers. In this sector, in fact, the relevance of the topological approach arises with glaring evidence producing important results that compete with ab-initio methods. The Wiener index may be used to investigate nanosystems with structural and topological defects. The presence of the bosonic quasi-particle is very well approximated by the inherent long-range topological nature of W.
