Application of graph theory and topological models for the determination of fundamentals of the aromatic character of pi-conjugated hydrocarbons

Application of topological analysis and graph theory to benzenoid hydrocarbons leads to the determination of fundamentals of aromaticity: the Hückel rule and the Clar rule. The approach, based on a treatment of the adjacency matrix, allows resonance energy (RE)-like characteristics to be estimated with quite good accuracy, and magnetic aromaticity indices to be derived for both the individual rings and the whole molecules. It also allows an effective approach for interpreting ring current formation in molecules when exposed to an external magnetic field. The transformation of the perturbation matrix into a form describing the canonical structures allows their gradation and determination of their stabilizing/destabilizing character.