Chemical Graph Theory

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Chemical Graph Theory

Author : D Bonchev
ISBN : 9781351461597
Genre : Science
File Size : 21.92 MB
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This volume presents the fundamentals of graph theory and then goes on to discuss specific chemical applications. Chapter 1 provides a historical setting for the current upsurge of interest in chemical graph theory. chapter 2 gives a full background of the basic ideas and mathematical formalism of graph theory and includes such chemically relevant notions as connectedness, graph matrix representations, metric properties, symmetry and operations on graphs. This is followed by a discussion on chemical nomenclature and the trends in its rationalization by using graph theory, which has important implications for the storage and retrieval of chemical information. This volume also contains a detailed discussion of the relevance of graph-theoretical polynomials; it describes methodologies for the enumeration of isomers, incorporating the classical Polya method, as well as more recent approaches.
Category: Science

Chemical Graph Theory

Author : Nenad Trinajstic
ISBN : 9781351461566
Genre : Science
File Size : 64.34 MB
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Chemical Graph Theory, 2nd Edition is a completely revised and updated edition of a highly regarded book that has been widely used since its publication in 1983. This unique book offers a basic introduction to the handling of molecular graphs - mathematical diagrams representing molecular structures. Using mathematics well within the vocabulary of most chemists, this volume elucidates the structural aspects of chemical graph theory: (1) the relationship between chemical and graph-theoretical terminology, elements of graph theory, and graph-theoretical matrices; (2) the topological aspects of the Hückel theory, resonance theory, and theories of aromaticity; and (3) the applications of chemical graph theory to structure-property and structure-activity relationships and to isomer enumeration. An extensive bibliography covering the most relevant advances in theory and applications is one of the book's most valuable features. This volume is intended to introduce the entire chemistry community to the applications of graph theory and will be of particular interest to theoretical organic and inorganic chemists, physical scientists, computational chemists, and those already involved in mathematical chemistry.
Category: Science

Chemical Graph Theory

Author : Danail Bonchev
ISBN : 0856265152
Genre : Science
File Size : 56.65 MB
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This volume is concerned with applications of graph theory to the study of chemical kinetics and reaction mechanisms. Methods of handling kinetic data are explained with emphasis on the derivation of rate laws and related problems. Graph-based classification and coding of reaction mechanisms along with approaches for determining their complexity are described, providing researchers with a useful tool in their search for new reaction mechanisms. The operator set approach to the structural and dynamic interrelations between chemical species is presented as a methodology for discovering new selection and prohibition rules. Also discussed are the reaction lattice technique and its application to aromaticity and pericyclic reactions, and the DARC/PELCO method, a topological tool for QSAR searching.
Category: Science

Chemical Reaction Networks

Author : Oleg N. Temkin
ISBN : 0849328675
Genre : Science
File Size : 40.37 MB
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Over the last decade, increased attention to reaction dynamics, combined with the intensive application of computers in chemical studies, mathematical modeling of chemical processes, and mechanistic studies has brought graph theory to the forefront of research. It offers an advanced and powerful formalism for the description of chemical reactions and their intrinsic reaction mechanisms. Chemical Reaction Networks: A Graph-Theoretical Approach elegantly reviews and expands upon graph theory as applied to mechanistic theory, chemical kinetics, and catalysis. The authors explore various graph-theoretical approaches to canonical representation, numbering, and coding of elementary steps and chemical reaction mechanisms, the analysis of their topological structure, the complexity estimation, and classification of reaction mechanisms. They discuss topologically distinctive features of multiroute catalytic and noncatalytic and chain reactions involving metal complexes. With it's careful balance of clear language and mathematical rigor, the presentation of the authors' significant original work, and emphasis on practical applications and examples, Chemical Reaction Networks: A Graph Theoretical Approach is both an outstanding reference and valuable tool for chemical research.
Category: Science

Introduction To Chemical Graph Theory

Author : Stephan Wagner
ISBN : 9780429833991
Genre : Mathematics
File Size : 87.46 MB
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Introduction to Chemical Graph Theory is a concise introduction to the main topics and techniques in chemical graph theory, specifically the theory of topological indices. These include distance-based, degree-based, and counting-based indices. The book covers some of the most commonly used mathematical approaches in the subject. It is also written with the knowledge that chemical graph theory has many connections to different branches of graph theory (such as extremal graph theory, spectral graph theory). The authors wrote the book in an appealing way that attracts people to chemical graph theory. In doing so, the book is an excellent playground and general reference text on the subject, especially for young mathematicians with a special interest in graph theory. Key Features: A concise introduction to topological indices of graph theory Appealing to specialists and non-specialists alike Provides many techniques from current research About the Authors: Stephan Wagner grew up in Graz (Austria), where he also received his PhD from Graz University of Technology in 2006. Shortly afterwards, he moved to South Africa, where he started his career at Stellenbosch University as a lecturer in January 2007. His research interests lie mostly in combinatorics and related areas, including connections to other scientific fields such as physics, chemistry and computer science. Hua Wang received his PhD from University of South Carolina in 2005. He held a Visiting Research Assistant Professor position at University of Florida before joining Georgia Southern University in 2008. His research interests include combinatorics and graph theory, elementary number theory, and related problems
Category: Mathematics

From Chemical Topology To Three Dimensional Geometry

Author : Alexandru T. Balaban
ISBN : 9780306469077
Genre : Science
File Size : 30.56 MB
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Even high-speed supercomputers cannot easily convert traditional two-dimensional databases from chemical topology into the three-dimensional ones demanded by today's chemists, particularly those working in drug design. This fascinating volume resolves this problem by positing mathematical and topological models which greatly expand the capabilities of chemical graph theory. The authors examine QSAR and molecular similarity studies, the relationship between the sequence of amino acids and the less familiar secondary and tertiary protein structures, and new topological methods.
Category: Science

Computational Chemical Graph Theory

Author : Nenad Trinajstić
ISBN : UOM:39015024777453
Genre : Science
File Size : 24.42 MB
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Based on the authors' own work, this book presents a computer-oriented method for the enumeration and generation of certain classes of chemical structures. The text is illustrated with block diagrams, computer programs and numerous tables with data for the classes of molecules considered.
Category: Science

Computational Chemical Graph Theory

Author : D. H. Rouvray
ISBN : STANFORD:36105030894765
Genre : Science
File Size : 22.97 MB
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The outcome of an American Chemical Society Conference Symposium held in Los Angeles, Sept. 1988. Chemical graph theory is a branch of mathematical chemistry that has concerned itself with the mathematical description and characterization of molecular species, notational schemes and the enumeration
Category: Science

Critical Issues In Mathematics Education

Author : Philip Clarkson
ISBN : 038756134X
Genre : Education
File Size : 84.72 MB
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Critical Issues in Mathematics Education presents the significant contributions of Professor Alan Bishop within the mathematics education research community. Six critical issues, each of which have had paramount importance in the development of mathematics education research, are reviewed and include a discussion of current developments in each area. Teacher decision making, spatial/visualizing geometry, teachers and research, cultural/social aspects of mathematics education, sociopolitical issues, and values serve as the basic issues discussed in this examination of mathematics education over the last fifty years during which Professor Bishop has been active in the field. A comprehensive discussion of each of these topics is realized by offering the reader a classic research contribution of Professor Bishop’s together with commentary and invited chapters from leading experts in the field of mathematics education. Critical Issues in Mathematics Education will make an invaluable contribution to the ongoing reflection of mathematic education researchers worldwide, but also to policy makers and teacher educators who wish to understand some of the key issues with which mathematics education has been and still is concerned, and the context within which Professor Bishop’s key contributions to these research issues were made.
Category: Education

Applications Of Graph Theory And Topology In Inorganic Cluster And Coordination Chemistry

Author : R. Bruce King
ISBN : 0849342988
Genre : Science
File Size : 59.12 MB
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Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry is a text-reference that provides inorganic chemists with a rudimentary knowledge of topology, graph theory, and related mathematical disciplines. The book emphasizes the application of these topics to metal clusters and coordination compounds. The book's initial chapters present background information in topology, graph theory, and group theory, explaining how these topics relate to the properties of atomic orbitals and are applied to coordination polyhedra. Subsequent chapters apply these ideas to the structure and chemical bonding in diverse types of inorganic compounds, including boron cages, metal clusters, solid state materials, metal oxide derivatives, superconductors, icosahedral phases, and carbon cages (fullerenes). The book's final chapter introduces the application of topology and graph theory for studying the dynamics of rearrangements in coordination and cluster polyhedra.
Category: Science

Quantitative Graph Theory

Author : Matthias Dehmer
ISBN : 9781466584525
Genre : Computers
File Size : 73.54 MB
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The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical technique
Category: Computers

Topology In Chemistry

Author : D H Rouvray
ISBN : 9780857099617
Genre : Science
File Size : 49.96 MB
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This volume addresses a number of topological themes of direct relevance to chemists. Topological concepts are now regularly applied in wide areas of chemistry including molecular engineering and design, chemical toxicology, the study of molecular shape, crystal and surface structures, chemical bonding, macromolecular species such as polymers and DNA, and environmental chemistry. Currently, the design and synthesis of new drugs and agrochemicals are of especial importance. The book's prime focus is on the role played by topological indices in the description and characterisation of molecular species. The Wiener index along with a variety of other major topological indices, are discussed with particular reference to the powerful and much used connectivity indices. In this book an international team of leading experts review their respective fields and present their findings. The considerable benefits offered by topological indices in the investigation of chemical problems in science, medicine, and industry are highlighted. The volume records proceedings of the Harry Wiener Memorial Conference on the Role of Topology in Chemistry, held at the University of Georgia in March 2001, and serves as a fitting tribute to the chemical contributions of the late Harry Wiener. Focuses on the role played by topological indices in the description and characterisation of molecular species Records the proceedings of the Harry Weiner Memorial Conference on the Role of Topology in Chemistry, held at the University of Georgia in March 2001 Along with a variety of other major topological indices, the Wiener index is discussed with particular reference to the powerful and much-used connectivity indices
Category: Science

Graph Theoretical Approaches To Chemical Reactivity

Author : Danail D. Bonchev
ISBN : UOM:39015032430137
Genre : Computers
File Size : 43.89 MB
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This is the first book to concentrate on elucidating chemical reactivity from the viewpoint of molecular topology. Describing the most fundamental structural patterns in molecules, topology and graph theory are regarded to be the ideal tools for exploring the relationships between the structure and the properties of chemical compounds. A team of internationally recognized experts from seven countries present a variety of graph-theoretical and topological approaches to chemical reactivity. The specific topics covered include among others, the latest developments in the interplay between graph theory and molecular orbital theory, three dimensional molecular shapes and their changes, isomerization reactions in organic and inorganic chemistry, topological indices and their application to structure-reactivity relationships and mechanistic studies. Useful topology-based reactivity rules and more general principles controlling topology changes in chemical reactions are also presented. For researchers, teachers and students in all areas of chemistry.
Category: Computers

Applications Graph Theory Topology In Inorganic Cluster Coordination Chemistry

Author : R. Bruce King
ISBN : 0849342988
Genre : Science
File Size : 90.86 MB
Format : PDF
Download : 351
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Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry is a text-reference that provides inorganic chemists with a rudimentary knowledge of topology, graph theory, and related mathematical disciplines. The book emphasizes the application of these topics to metal clusters and coordination compounds. The book's initial chapters present background information in topology, graph theory, and group theory, explaining how these topics relate to the properties of atomic orbitals and are applied to coordination polyhedra. Subsequent chapters apply these ideas to the structure and chemical bonding in diverse types of inorganic compounds, including boron cages, metal clusters, solid state materials, metal oxide derivatives, superconductors, icosahedral phases, and carbon cages (fullerenes). The book's final chapter introduces the application of topology and graph theory for studying the dynamics of rearrangements in coordination and cluster polyhedra.
Category: Science

Graph Theory 1736 1936

Author : Norman Biggs
ISBN : 0198539169
Genre : Mathematics
File Size : 47.93 MB
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First published in 1976, this book has been widely acclaimed both for its significant contribution to the history of mathematics and for the way that it brings the subject alive. Building on a set of original writings from some of the founders of graph theory, the book traces the historical development of the subject through a linking commentary. The relevant underlying mathematics is also explained, providing an original introduction to the subject for students. From reviews: 'The book...serves as an excellent examplein fact, as a modelof a new approach to one aspect of mathematics, when mathematics is considered as a living, vital and developing tradition.' (Edward A. Maziark in Isis) 'Biggs, Lloyd and Wilson's unusual and remarkable book traces the evolution and development of graph theory...Conceived in a very original manner and obviously written with devotion and a very great amount of painstaking historical research, it contains an exceptionally fine collection of source material, and to a graph theorist it is a treasure chest of fascinating historical information and curiosities with rich food for thought.'(Gabriel Dirac in Centaurus) 'The lucidity, grace and wit of the writing makes this book a pleasure to read and re-read.' (S. H. Hollingdale in Bulletin of the Institute of Mathematics and its Applications)
Category: Mathematics

The Mathematics And Topology Of Fullerenes

Author : Franco Cataldo
ISBN : 9400702213
Genre : Science
File Size : 73.85 MB
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The Mathematics and Topology of Fullerenes presents a comprehensive overview of scientific and technical innovations in theoretical and experimental studies. Topics included in this multi-author volume are: Clar structures for conjugated nanostructures; counting polynomials of fullerenes; topological indices of fullerenes; the wiener index of nanotubes; toroidal fullerenes and nanostars; C60 Structural relatives: a topological study; local combinatorial characterization of fullerenes; computation of selected topological indices of C60 and C80 Fullerenes via the Gap Program; 4valent- analogues of fullerenes; a detailed atlas of Kekule structures of C60. The Mathematics and Topology of Fullerenes is targeted at advanced graduates and researchers working in carbon materials, chemistry and physics.
Category: Science

Mathematical Chemistry

Author : Wei Inu Hong
ISBN : 1608768945
Genre : Science
File Size : 40.67 MB
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Mathematical chemistry is the area of research engaged in the novel applications of mathematics to chemistry; it concerns itself principally with the mathematical modelling of chemical phenomena. Mathematical chemistry has also sometimes been called computer chemistry, but should not be confused with computational chemistry. Major areas of research in mathematical chemistry include chemical graph theory, which deals with topics such as the mathematical study of isomerism and the development of topological descriptors or indices which find application in quantitative structure-property relationships; chemical aspects of group theory, which finds applications in stereochemistry and quantum chemistry; and topological aspects of chemistry.
Category: Science