How can we explain the stability of conjugated hydrocarbon-and heterosubstituted networks by topological descriptors?

Correlation between the π-electronic stability (Hückel's Eπ) and several topological descriptors, including Hosoya's Z, Wiener's W, and Randic's 1χ , was compared for the isomeric acyclic conjugated hydrocarbon molecules from hexatriene to decapentaene. From the analysis of the best descriptor Z and mean length of conjugated paths L, the origin of π-electronic stability was logically explained. The effect of heteroatom substitution to polyenes was studied and analyzed by graph-theoretical techniques. The difference in the stability and electron flow for this heteroatom substitution was also quantitatively and easily explained. Discussion was given for the difference in the topological dependency of HOMO level of these networks with even and odd number of skeletal carbon atoms. An efficient determinantal method for calculating the Z-index for tree graphs is introduced.