The structural relationship between Randić indices, adjacency matrixes, distance matrixes and maximum wave length of linear simple conjugated polyene compounds

Graph theory provides the useful natural mathematical frameworks for the quantitative codification of classical chemical bonding ideas. One of the useful indices for examination of structure-property relationship is Randić index. In this study, is represented the relationship between the Randić index, the determinants of the adjacency matrix and distance matrix to maximum wave length (λmax) of the linear simple conjugated polyenes. The alternative double bonds and conjugation in the polyene compounds are one of the main properties in these compounds. Some of the properties here considered are associated with the molecular orbital method include and λmax, the electrical conductivity and the difference energy level of the HOMO and LUMO orbitals (ΔE). For calculation the λmax of the compounds could use the Fieser-Kuhn rule. The interesting results of concerning among λmax and the above indices are presented.