Topological Organic Chemistry, 9. Graph Theory and Molecular Topological Indices of Stereoisomeric Organic Compounds

papers of this series’ reported the use of distance (D) matrices as sources of molecular topological indices for a variety of homonuclear (carbon) and heteronuclear organic compounds. Although numerous authors referred to in past papers of this sequence have gathered references, reviewed papers, and created new avenues of approach to all facets of the above topics, few have been concemed with the stereochemistry of organic substances. Shelly .and Munk2 and Barnard et alS3 and their included references overviewed the subject to 1989. Since then some seminal papers on the theme have been published by Akutsu? Razinger et al.: Agarwal and Gelemter? Mata and Lobo,’ and Pogliani8 Most of these have been concemed with the sophishated objective of devising algorithms for total molecular notations of molecules possessing stereocenters. This paper reports the results of experiments directed toward means to represent the kinds of stereocenters present in homonuclear and heteronuclear organic molecules as well as to recognize the influences of the stereocenters on the values of the molecular topological indices examined in detail in prior papers of this set’-MTI’, product of row sums, determinant, permanent, and long hafnian. These experiments were focused on two broad facets of stereochemistry. First: the isomerism that exists as a consequence of restricted rotation in appropriately substituted cyclic systems, including cycloethane (ethene). The isomerism that obtains in such systems is referred to in this article as geometrical isomerism. Second: the isomerism which is due to the presence of stereocenter@) in some organic compounds-centers that may confer “handedness” or chirality upon molecules. Such substances are designated as optical isomers in this paper.