The pioneering contributions of cayley and sylvester to the mathematical description of chemical structure

Abstract

The foundations of modern chemical graph theory were laid by the pioneering work of the mathematicians Arthur Cayley (1821–1895) and James Sylvester (1814–1897). In attempting to characterize chemical structure in purely mathematical terms, they established that an isomorphism exists between the structures of individual chemical molecules and mathematical graphs. They thereby first demonstrated the relevance of the graph in the chemical context. Cayley made use of graphs in the enumeration of constitutional isomers for the members of the alkane and other homologous series, whereas Sylvester employed graphs for both the depiction of molecules and the derivation of polynomial expressions thought to be characteristic of chemical structures. The long-term impact of their work is now seen to have been immense. In particular, recent years have witnessed a dramatic growth in the various applications of chemical graph theory. Papers exploiting the concept of the chemical graph are currently appearing at the rate of almost 600 per annum.