Information theory, distance matrix, and molecular branching

Information theory was used in defining several measures of the topological properties of molecules, namely, information for adjacency, incidence, polynomial coefficients of the adjacency matrix, and for distances of molecular graphs. The latter was found to have a greater ability for discrimination between structural isomers than all known topological indices and to be a very appropriate measure of branching. All the quantities related to the distance matrix (two information measures, the Weiner number and the largest eigenvalue of the characteristic polynomial) were found to reflect in the same way the main features of molecular branching. On this basis, as well as on the basis of general expressions for information content and Wiener number derived for tree graphs, the essence of molecular branching was expressed in a number of rules. It was shown that these theoretical rules on branching are in agreement with the intuitive understanding of branching and are reflected in a large number of molecular properties.