DESIGN OF MOLECULES FROM QUANTITATIVE STRUCTURE-ACTIVITY RELATIONSHIP MODELS .3. ROLE OF HIGHER-ORDER PATH COUNTS - PATH-3

The development of the inverse imaging process is continued here with attention given to the role of the count of paths of length 3 in molecular graphs. The relation between path counts and edge type counts is developed for paths of length 0, 1, 2, and 3. A general relation is developed among the edge type counts which places significant restrictions upon the edge types which can constitute a molecular graph. Independent equations are derived for relations among the edge types and path counts. A method for generating and validating edge type counts is presented for the nine edge types encountered in molecular graphs, including those for acyclic and cyclic molecules. These relations are applied to the generation of molecular graphs which represent molecules with molar volumes in a specified range of values as was done in part 1 using only path counts 0, 1, and 2. This development extends the inverse process to include the path 3 count.