GRAPH THEORETICAL ORDERING OF STRUCTURES AS A BASIS FOR SYSTEMATIC SEARCHES FOR REGULARITIES IN MOLECULAR-DATA

Selected molecular data on alkanes have been reexamined in a search for general regularities in isomeric variations. In contrast to the prevailing approaches concerned with fitting data by searching for optimal parameterization, the present work is primarily aimed at established trends, i.e., searching for relative magnitudes and their regularities among the isomers. Such an approach is complementary to curve fitting or correlation seeking procedures. It is particularly useful when there are incomplete data which allow trends to be recognized but no quantitative correlation to be established. One proceeds by first ordering structures. One way is to consider mokicular graphs and enumerate paths of different length as the basic graph invariant. It can be shown that, for several thermodynamic molecular properties, the number of paths of length two (p2) and length three (p3) are critical. Hence, an ordering based on p2 and p3 indicates possible trends and behavior for many molecular properties, some of which relate to others, some which do not. By considering a grid graph derived by attributing to each isomer coordinates (p2,P3) and connecting points along the coordinate axis, one obtains a simple presentation useful for isomer structural interrelations. This skeletal frame is one upon which possible trends for different molecular properties may be conveniently represented. The significance of the results and their conceptual value is discussed. © 1979 American Chemical Society.