ABSTRACT
Department of Organic Chemistry, Faculty of Industrial Chemistry, Oficiul 12 CP 243, 78100 Bucharest, Romania
Organic compounds containing heteroatoms and/or multiple bonds can be conveniently represented as vertex-and edge-weighted molecular graphs. From the several hundreds topological indices introduced for molecular graphs, the large majority are defined only for simple graphs that represent alkanes and cycloalkanes. A large number of mathematical relationships were discovered for the graph descriptors of alkanes and cycloalkanes, and thus chemists made important contributions to the graph theory. Apart from the mathematical beauty of such theorems and relationships, the main chemical application of topological indices remains that of structural descriptors in structure-property and structure-biological activity models. Such studies require the computation of topological indices for molecular graphs containing heteroatoms and multiple bonds. The main schemes proposed for computing the vertex-and edge-weighted graph parameters are reviewed and some examples are provided for the generation of the most important weighted graph matrices. The computation of polynomials, spectra, and spectral moments for weighted graph matrices is given, with examples for various organic compounds. Vertex-and edge-weighted molecular graphs matrices are the source of atomic structural descriptors; those that gained a wider use are presented. Using various mathematical operations weighted graph matrices, their polynomials and spectra are transformed into topological indices; the most important ones are reviewed.
