Topological Indies as Chemical Behavior Descriptors.
GEORGIA UNIV ATHENS DEPT OF CHEMISTRY
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Graph theorists have contributed steadily to the development of chemistry since the pioneering work of Arthur Cayley on isomer enumeration in the mid-1870s. Their contributions, however, have been confined mainly to one or two applications only. After briefly reviewing the principal applications of graph theory and combinatorics in chemistry, it is pointed out that there are still numerous interesting mathematical problems waiting to be tackled. A number of these involve the various graph invariants used by chemists to characterize molecular graphs in this context such invariants are usually referred to as topological indices TIs. Many different TIs have been put forward to date and most have been employed to characterize chemical behavior dependent upon either a molecular size, b molecular shape, c specific molecular sites within a molecule. Three comparatively simple TIs based on the distance matrix are exhibited. The first of these has been used to predict the physicochemical properties of hydrocarbon molecules the second, properties which depend on the degree of branching present in molecules such as the octane number of fuels and the third, the occurrence of carcinogencity, mutagenicity or tetratogencity in polycyclic aromatic speciespolyhexes. Current work on TIs and some of the mathematical problems associated with their further development are briefly outlined.
- Atomic and Molecular Physics and Spectroscopy