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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 a

"Distance metrics and distances have become an essential tool in many areas of pure and applied Mathematics, and this encyclopedia is the first one to treat the subject in full. The book appears just

Figurate numbers have a rich history with many applications. The main purpose of this book is to provide a thorough and complete presentation of the theory of figurate numbers, giving much of their pr

This book comes out of need and urgency (expressed especially in areas of Information Retrieval with respect to Image, Audio, Internet and Biology) to have a working tool to compare data.The book wil

This book introduces oriented version of metrics and cuts and their multidimensional analogues, as well as partial metrics and weighted metrics. It is a follow-up of Geometry of Cuts and Metrics by De

Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers

Deza (Ecole Normale Superieure and CNRS, Paris) Viatcheslav Grishakhin (Central institute of Mathematical Economics, Moscow), and Kikhail Shtogrin (Stedlov Mathematical Institute, Moscow) identify com

The central theme of the present book is zigzags and central-circuitsof three- or four-regular plane graphs, which allow a double covering or covering of the edgeset to be obtained. The book presents