Minimally Kekulenoid -Networks and Reactivity for Acyclics*

Mathematical chemistry has been formally recognized only during just the last few decades, with a strong influence involving graph theoretic work. This special influence is perhaps quite appropriate in view of its relevance in the classical core of chemistry, the characterization of molecular structure, and valence theory. Indeed the mathematical field of graph theory may be surmised to take its name from usage in chemistry. In particular J. J. Sylvester1 in 1878 introduces the terminology of »graph« in mathematics in an article exuberantly reveling in the possible applications in chemistry where already the phrase »graphical representation« was in frequent use in describing the molecular structural formulas with which Sylvester was so deeply intrigued. Near simultaneously A. Cayley (who was a friend of Sylvester’s) made2 a notable application to enumeration of alkyl radicals and alkanes. But mathematical graph theory was not then well developed, and Sylvester’s idea of a close interaction between mathematics and chemistry remained a dream, though there were a few isolated cases where Sylvester and Cayley’s ideas were sought to be pursued.3 Also in the mid 1930s G. Polya4 further sought chemo-mathematical symbiosis, again through the use of graph theory, and ended up developing a mathematically fundamental combinatorial enumeration under group action, though again for a while the impact on chemistry was marginal. Starting in the 1930s E. H ckel, C. A. Coulson, and a host of other theoretical chemists developed a simple quantum mechanical »molecular-orbital« model of molecular electronic structure, which especially for conjugated -networks entailed many graph-theoretically based ideas, though little inspiration was drawn from matheCROATICA CHEMICA ACTA CCACAA 77 (1–2) 179¿191 (2004)