By Michel-Marie Deza, Mathieu Dutour Sikirić, Mikhail Ivanovitch Shtogrin

ISBN-10: 8132224485

ISBN-13: 9788132224488

ISBN-10: 8132224493

ISBN-13: 9788132224495

Discusses zigzag and vital circuit buildings of geometric fullerenes

Introduces the symmetries, parameterization and the Goldberg-Coxeter development for chemistry-relevant graphs

Presents state-of-the paintings content material at the topic

Written via revered authors and specialists at the subject

Will be necessary to researchers and scholars of discrete geometry, mathematical chemistry, and combinatorics, in addition to to put mathematicians

The vital subject of the current publication is zigzags and central-circuits of 3- or four-regular airplane graphs, which enable a double masking or overlaying of the edgeset to be acquired. The booklet provides zigzag and crucial circuit buildings of geometric fullerenes and several sessions of graph of curiosity within the fields of chemistry and arithmetic. It additionally discusses the symmetries, parameterization and the Goldberg-Coxeter development for these graphs.

It is the 1st e-book in this topic, offering complete constitution thought of such graphs. whereas many past guides merely addressed specific questions on chosen graphs, this ebook relies on various computations and provides vast information (tables and figures), in addition to algorithmic and computational details. will probably be of curiosity to researchers and scholars of discrete geometry, mathematical chemistry and combinatorics, in addition to to put mathematicians.

Topics

Graph Theory

Mathematical purposes within the actual Sciences

Math. purposes in Chemistry

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**Extra resources for Geometric Structure of Chemistry-Relevant Graphs: Zigzags and Central Circuits**

**Example text**

5). Any other belt, which has no common interior point with the 1-st belt, is inside one of these disks. If two belts have no common boundary points, then there is a cylinder (an annulus) between them consisting only of 6-gons. 2, this cylinder contains a sequence of belts in which two neighbors are adjacent along a zigzag. The belts in this sequence fill another cylinder. 2. We join this belt to the cylinder. After a finite number of steps, we obtain a cylinder with only 5-gons adjacent to its boundary from outside.

The star of C consists of the 2-nd 5-gon, the 3-rd 5-gon, and some 4-th 5-gon. The 4-th and 3-rd 5-gons have a common edge CD, and so on. The sequence ABCD . . can be continued indefinitely. ) Again, we end up with a contradiction. In a thimble, pairs of edges of boundary 5-gons with a common vertex, which is opposite to a boundary edge of a 5-gon, form a simple zigzag, because all faces adjacent to the boundary of a thimble are different 5-gons. If all the boundary faces of an c − DF are 5-gons, but the c − DF is not a thimble (see one in Fig.

18. See also first and seventh fullerenes on Fig. 3: a 5-thimble F30 (D5h ) (with z = 102 , 7015,10 and a belt of five 6-gons) reduces to 5-thimble F20 (Ih ) with z = 106 and pure 6-thimble F36 (D6h ) (with z = 122 , 146 and 6-belt) reduces to 6-thimble F24 (D6d ) with z = 12; 6012,12 . A disk-fullerene with a simple zigzag Z can be extended by cutting it into two parts along Z and inserting a belt joining them. The extending operation is the reverse of the reduction operation and is also not uniquely defined.

### Geometric Structure of Chemistry-Relevant Graphs: Zigzags and Central Circuits by Michel-Marie Deza, Mathieu Dutour Sikirić, Mikhail Ivanovitch Shtogrin

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