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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.