Geometry of Chemical Graphs

Erscheinungsjahr 2008
ISBN: 978-0-521-87307-9
Verlag: Cambridge University Press

Buch, Englisch, Band 119, 318 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 643 g

Reihe: Encyclopedia of Mathematics and its Applications

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.

Autoren/Hrsg.

Deza, Michel

Dutour Sikiri¿, Mathieu

Dutour Sikiric, Mathieu

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research Graphentheorie
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

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.

Über Autor(innen)

Dutour Sikiric, Mathieu
Mathieu Dutour Sikiric is a Researcher of Mathematics at Institut Rudjer Boškovic, Zagreb. His research interests include enumeration and extremal problems, in relation to plane graph and discrete structures; polyhedral enumeration, Lattices, Delaunay polytopes and dual description problems.

Deza, Michel
Michel Deza is Director of Research at CNRS, Director of the Laboratoire interdisciplinaire de géométrie appliquée, and a Professor at Ecole Normale Supérieure, Paris. He is Editor-in-chief of the European Journal of Combinatorics and this is his 12th book.