Geometry of Chemical Graphs
Polycycles and Two-faced Maps

Mathematical tools for the study of generalisations of graphs appearing in the modelling of molecular structures.

Michel Deza (Author), Mathieu Dutour Sikiri? (Author)

9780521873079, Cambridge University Press

Hardback, published 26 June 2008

316 pages, 295 b/w illus. 3 colour illus. 15 tables
24.1 x 16.5 x 2.4 cm, 0.61 kg

'… a rich source of chemical graphs (and beyond) and their properties. It should thus serve as a standard reference for researchers in the area.' Mathematical Reviews

Polycycles and symmetric polyhedra appear as generalisations of graphs in the modelling of molecular structures, such as the Nobel prize winning fullerenes, occurring in chemistry and crystallography. The chemistry has inspired and informed many interesting questions in mathematics and computer science, which in turn have suggested directions for synthesis of molecules. Here the authors give access to new results in the theory of polycycles and two-faced maps together with the relevant background material and mathematical tools for their study. Organised so that, after reading the introductory chapter, each chapter can be read independently from the others, the book should be accessible to researchers and students in graph theory, discrete geometry, and combinatorics, as well as to those in more applied areas such as mathematical chemistry and crystallography. Many of the results in the subject require the use of computer enumeration; the corresponding programs are available from the author's website.

Preface
1. Introduction
2. Two-faced maps
3. Fullerenes as tilings of surfaces
4. Polycycles
5. Polycycles with given boundary
6. Symmetries of polycycles
7. Elementary polycycles
8. Applications of elementary decompositions to (r, q)-polycycles
9. Strictly face-regular spheres and tori
10. Parabolic weakly face-regular spheres
11. Generalities on 3-valent face-regular maps
12. Spheres and tori, which are aRi
13. Frank-Kasper spheres and tori
14. Spheres and tori, which are bR1
15. Spheres and tori, which are bR2
16. Spheres and tori, which are bR3
17. Spheres and tori, which are bR4
18. Spheres and tori, which are bRj for j ? 5
19. Icosahedral fulleroids.

Subject Areas: Quantum & theoretical chemistry [PNRP], Combinatorics & graph theory [PBV], Geometry [PBM]