Neighborhood Complexities and Symmetry of Chemical Graphs and Their Biological Applications

Quantitative Structure−Property Relationships (QSPRs) for the Estimation of Vapor Pressure: A Hierarchical Approach Using Mathematical Structural Descriptors

“…Of the 476 chemicals in the original data set, seven were two-atom compounds and thus not included in the present study due to the fact that the triplet indices, which are described in the following section, cannot be calculated for two-atom compounds. The molecular weights of the compounds in this data set range from 40 to 338, and the chemical diversity is described in Table 1 23 The topological descriptors include Wiener number, 24 molecular connectivity indices developed by Randić 25 and Kier and Hall, 26 frequency of path lengths of varying size, 26 information theoretic indices defined on distance matrices of graphs using the methods of Bonchev and Trinajstić, 27 Roy et al, 28 as well as those of Raychaudhury et al, 33 parameters defined on the neighborhood complexity of vertices in hydrogen-filled molecular graphs, 29-33 a simple hydrogen bonding parameter, 23 and Balaban's J indices 34 as well as the triplet indices. 35,36 The triplets result from a matrix, main diagonal column vector, and free term column vector which are converted into a system of linear equations.…”

A Comparative Study of Topological and Geometrical Parameters in Estimating Normal Boiling Point and Octanol/Water Partition Coefficient

“…40 These indices include the molecular connectivity indices developed by Randić 18 and Kier and Hall, 35 Wiener number, 41 and frequency of path lengths of varying size. Information theoretic indices defined on the hydrogen-filled and hydrogen-suppressed molecular graph were calculated by POLLY using the methods of Basak et al, 42,43 Roy et al, 44 Raychaudhury et al, 45 and Bonchev and Trinajstić. 46 The J indices of Balaban [47][48][49] were calculated using software developed by the authors.…”

Applications of Topological Indices in the Property/Bioactivity/Toxicity Prediction of Chemicals

“…(1978) where v runs over the whole vertex set V(G), forms a neighborhood system of the vertices of G. A suitably defined equivalence relation can then partition V(G) into disjoint subsets based on the topological neighborhoods of vertices up to r'l'order neighbors. Such an approach has already been initiated and the information-theoretic indices calculated are called indices of neighborhood symmetry (Magnuson et af., 1983;Roy et al, 1984).…”