An innovative theoretical mechanism leading to the classification of the
stability of fullerene isomers is presented. This approach is based on the action of
suitable topological potentials impacting on molecular stability, namely topological
compactness and topological sphericality indexes, providing a fast and general ranking
algorithm. Present results point out that electronic properties of sp2 carbon systems are
deeply rooted in the topology of their atomic network.
Keywords: C50 fullerene, chemical distance, chemical graph, DFT, energy
ranking algorithm, fullerene stability, graph invariants, long-range connectivity
effects, minimal vertices, schlegel graphs, sp2 carbon systems, topological
compactness, topological efficiency index, topological modeling, topological
potential, topological sphericality, wiener index, wiener-weights, π-electron
energy.
