Geometric Structure of Chemistry-Relevant Graphs: Zigzags and Central Circuits [Hardcover]

The central theme of the present book is zigzags and central-circuits of three- or four-regular plane graphs, which allow a double covering or covering of the edgeset to be obtained. The book presents zigzag and central circuit structures of geometric fullerenes and several other classes of graph of interest in the fields of chemistry and mathematics. It also discusses the symmetries, parameterization and the GoldbergCoxeter construction for those graphs.

It is the first book on this subject, presenting full structure theory of such graphs. While many previous publications only addressed particular questions about selected graphs, this book is based on numerous computations and presents extensive data (tables and figures), as well as algorithmic and computational information. It will be of interest to researchers and students of discrete geometry, mathematical chemistry and combinatorics, as well as to lay mathematicians.

Chapter 1. Introduction: main ZC-notions.- Chapter 2. Zigzags of fullerenes and c-disk-fullerenes.- Chapter 3. Zigzags and railroads of spheres 3_v and 4_v.- Chapter 4. ZC-circuits of 4-regular and self-dual {2,3,4}-spheres.- Chapter 5. ZC-circuits of 5- and 6-regular spheres.- Chapter 6. GoldbergCoxeter construction and parametrization.- Chapter 7. ZC-circuits of GoldbergCoxeter construction.- Chapter 8. Zigzags of polytopes and complexes.

MICHEL-MARIE DEZA is former research director at the French National Research Centre and Ecole Normale Sup?rieure, Paris. Earlier, he was research professor at the Japan Advanced Institute of Science and Technology. He is author of about 300 research publications on discrete geometry, combinatorics and their applications to chemistry and crystallography. He is lcĄ