By Alexandru T. Balaban

ISBN-10: 0120760509

ISBN-13: 9780120760503

Shipped from united kingdom, please let 10 to 21 enterprise days for arrival. Chemical purposes of graph conception, hardcover, solid, Ex-Library: comprises the standard stamps and markings. The airborne dirt and dust jacket has a few scuffs and marks. another way there is not any harm to the covers, pages or backbone.

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**Extra resources for Chemical applications of graph theory**

**Example text**

S2m)9 . . , Z(H\ Sn , S2n, S^n • • • 5m«)) 9 9 (3*6) It will be seen that the group of permutations of the elements R 1? 5) is obtained in just this way, taking G and H to be S 2. Hence it is the wreath product S 2 [S2 ]. 6) instead. This is akin to using a steam-hammer to crack a nut, but it will serve to demonstrate the mechanism of the hammer. In Z(G) = 1/i(sl + s 2) we have to replace each occurrence of s x by Z{H) = Vi(s\ + s2)9and each occurrence of s2 by Vi (s2 + s4). We then have Z(S2 [s2 ]) = M s ] +s2) V + = Vs{^i + [Hs + 2s\+3 We can now resume the enumeration that we interrupted in order to define the wreath product.

Paris, 201, 1167. 5. , (1936). Sur le nombre des isomeres de certains composes chimiques, Compt. rend. Acad. Sci. Paris, 202, 1554. 6. , (1936). Uber das Anwachsen des Isomerenzahlen in den homologen Reihen des organischen Chemie, Vierteljschr. Naturforsch. Ges. Zurich, 81, 243. 7. , (1874). On the mathematical theory of isomers, Philos. Mag. 67, 444. 8. Blair, C. M. and Henze, H. , (1931). The number of structurally isomeric alcohols of the methanol series,/. Amer. Chem. Soc. 53, 3042. 9. , (1948).

Now consider all permutations of the mn elements of M that can be obtained in the following way: (a) For each row of M choose a permutation belonging to H , and permute 34 4. ENUMERATION OF ACYCLIC CHEMICAL COMPOUNDS the elements of that row by that permutation. The permutations for the various rows are chosen independently; they need not be all the same, nor need they all be different. (b) Having permuted each row according to the permuatation chosen for it now permute the rows among themselves by a permutation belonging to G.

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