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Geometry of Chemical Graphs: Polycycles and Two-faced Maps
     

Geometry of Chemical Graphs: Polycycles and Two-faced Maps

by Michel Deza, Mathieu Dutour Sikiric
 

ISBN-10: 052187307X

ISBN-13: 9780521873079

Pub. Date: 07/14/2008

Publisher: Cambridge University Press

Polycycles and symmetric polyhedra appear as generalizations of graphs in the modeling 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

Overview

Polycycles and symmetric polyhedra appear as generalizations of graphs in the modeling 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. Organized 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.

Product Details

ISBN-13:
9780521873079
Publisher:
Cambridge University Press
Publication date:
07/14/2008
Series:
Encyclopedia of Mathematics and its Applications Series , #119
Pages:
316
Product dimensions:
6.14(w) x 9.21(h) x 0.94(d)

Table of Contents

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.

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