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Wyznaczanie liczby izomerów: od Cayleya do nanorurek

Dobrowolski J.Cz.

Wiadomości Chemiczne

2006

[Z] 60, 3-4

171-190

Chemical graph theory is a dynamically developing area of mathematical chemistry which is taught at Chemistry Departments of Polish Universities only seldomly. Especially, molecular graph enumeration, which is one of the oldest branch of chemical graph theory, begun by English mathematician Arthur Cayley's work On the Mathematical Theory ofisomers published in 1874, will always support and stimulate progress of chemistry. In this review, the most important theorem for graph enumeration, known as Pólya Hauptsatz, proven in 1930s by Hungarian and American mathematician George Pólya (1887-1985), is only illustrated. The review remainds early Henze i Blair results of alkanes enumerations as well as quite modern Robinson, Harary, and Balaban enumeration of chiral alkanes. Selected results found for benzenoid hydrocarbons are presented and through the famous Euler polyhedron rule a connection with enumeration of fullerenes and nanotubes is shown.

Metody matematyczne w chemii : wybrane zastosowania teorii grafów

Nowakowski J.

Wiadomości Chemiczne

2000

[Z] 54, 5-6

371-388

The mathematization of chemistry has a long history. In 1874 Brown, one of the great pioneers of chemical structure theory, prophesied that " ... chemistry will become a branch of applied mathematics ... and enable to justify results obtained by experiment and predict entirely novel discoveries". This prophesy was soon to be fulfilled. In 1875 the British mathematician Cayley enumerated both the isomers of alkanes and alkyl radicals based on the graph theory. He realized that chemical graphs could be used to present molecules because of the isomorphism that exists between such graphs and molecular structures. This relation plays an important role in application of the graph theory in modern chemistry. In the article a brief description of the results in the field of enumeration and generation of isomers is given. The connections between chemical terms and quantities of mathematical graph theory are shown. Illustrative examples, are chosen and mathematical principles of the methods are presented. Recent papers on enumeration of isomers are compiled. The topological matrix in Hückel molecular orbital method is isomorphic with the adjacency matrix of molecular graph. Isospectral graphs within the Hückel molecular orbital method correspond to conjugated molecules having the same set of orbital energies and related physical and chemical properties. Therefore the generation of isospectral graphs may be used to find similar chemical compounds. The methods of such generation based on some quantumchemical and informative characteristics are described. Computers enable today the practical use of the mathematical methods mentioned in the article. Even the personal computers are useful in the topic. Some calculations can be done on-line by Internet or with the use of commercial computer programs.