DESIGN OF MOLECULES FROM QUANTITATIVE STRUCTURE-ACTIVITY RELATIONSHIPMODELS .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 molec ular 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 de veloped among the edge type counts which places significant restrictio ns upon the edge types which can constitute a molecular graph. Indepen dent equations are derived for relations among the edge types and path counts. A method for generating and validating edge type counts is pr esented for the nine edge types encountered in molecular graphs, inclu ding those for acyclic and cyclic molecules. These relations are appli ed to the generation of molecular graphs which represent molecules wit h molar volumes in a specified range of values as was done in part 1 u sing only path counts 0, 1, and 2. This development extends the invers e process to include the path 3 count.