Chemical Graphs and Cambridge.

Euromug attendees may be interested in the fact that the famous mathematician, Arthur Cayley (1821-1895) worked at Trinity College, just a short walk from the hotel. Indeed one of the conference suites in the hotel is named after him. His work on algebraic matrices served as a foundation for Heisenberg's development of quantum chemistry in 1925.

Of more direct relevance to attendees was his construction of "kenograms" ( A. Cayley Phil. Mag. 47(1874), 444) which were alkane tree graphs; these were used in the enumeration of the alkane structural isomers. Examples of these trees are shown in a picture reproduced from Dennis Rouvray's "The Origins of Chemical Graph Theory" ( Mathematical Chemistry 1(1991), 1-39).

( I am not sure what the semantics of * were in this particular release of the Daylight software J ).

Cayley was the first to employ generating functions in isomer enumeration work. In Rouvray's excellent history he goes on to describe how " he (Cayley), in 1857 (A. Cayley Phil. Mag. 13(1857), 172) had devised a method for enumerating rooted trees Using this function he succeeded in 1874 in enumerating unrooted trees which correspond to alkane molecules. He obtained isomer counts for alkanes up to the thirteenth member of the series, though his results for the latter two were shown to be erroneous. By 1875, Cayley had published a lengthy paper (A. Cayley, Rept. Brit. Assoc. Adv. Sci. 257 (1875)) wherein he considered trees representing molecules in which the maximum valence of the atoms was four. He considered not only the alkanes, but also so called 'boron trees' (maximum valence three) and 'oxygen trees' (maximum valence two). He also presented isomer counts for the alkyl radicals up to the thirteenth member."

More can be found about Cayley at

Another famous son of Trinity College was Charles Babbage who was responsible for the forerunner of the modern computer. So in Cambridge we have the roots of much of chemical information systems we use today.

You can find information about other alumni of Trinity at