Geometric Structure of Chemistry-Relevant Graphs PDF Download
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Author: Michel-Marie Deza
Publisher: Springer
ISBN: 8132224493
Category : Mathematics
Languages : en
Pages : 220
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Book Description
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 Goldberg–Coxeter 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.
Author: Michel-Marie Deza
Publisher: Springer
ISBN: 8132224493
Category : Mathematics
Languages : en
Pages : 220
Get Book Here
Book Description
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 Goldberg–Coxeter 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.
Author: D Bonchev
Publisher: Taylor & Francis
ISBN: 1351461605
Category : Science
Languages : en
Pages : 301
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Book Description
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.
Author: D Bonchev
Publisher: CRC Press
ISBN: 9780856264542
Category : Science
Languages : en
Pages : 310
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Book Description
Initiates an ongoing series intended to consider a wide range of topics related to the mathematics of chemistry. Presents the fundamentals of graph theory and specific chemical applications of its. The topics include historical background, basic ideas and mathematical formalism, graph theory's influence in the rationalization of chemical nomenclature, graph-theoretical polynomials, and the interplay with molecular orbital theory in terms of graph spectral theory and topological resonance. Suitable for advanced undergraduates, graduates, and professionals. Acidic paper. Book club price, $52. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Nenad Trinajstic
Publisher: Routledge
ISBN: 1351461567
Category : Science
Languages : en
Pages : 268
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Book Description
New Edition! Completely Revised and Updated 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.
Author: Danail D. Bonchev
Publisher: Springer Science & Business Media
ISBN: 9401112029
Category : Science
Languages : en
Pages : 291
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Book Description
The progress in computer technology during the last 10-15 years has enabled the performance of ever more precise quantum mechanical calculations related to structure and interactions of chemical compounds. However, the qualitative models relating electronic structure to molecular geometry have not progressed at the same pace. There is a continuing need in chemistry for simple concepts and qualitatively clear pictures that are also quantitatively comparable to ab initio quantum chemical calculations. Topological methods and, more specifically, graph theory as a fixed-point topology, provide in principle a chance to fill this gap. With its more than 100 years of applications to chemistry, graph theory has proven to be of vital importance as the most natural language of chemistry. The explosive development of chemical graph theory during the last 20 years has increasingly overlapped with quantum chemistry. Besides contributing to the solution of various problems in theoretical chemistry, this development indicates that topology is an underlying principle that explains the success of quantum mechanics and goes beyond it, thus promising to bear more fruit in the future.
Author: Michel Deza
Publisher:
ISBN: 9781107096042
Category :
Languages : en
Pages : 318
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Book Description
Mathematical tools for the study of generalisations of graphs appearing in the modelling of molecular structures.
Author: Michel Deza
Publisher:
ISBN: 9781306148672
Category :
Languages : en
Pages :
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Book Description
Mathematical tools for the study of generalisations of graphs appearing in the modelling of molecular structures.
Author: D. H. Rouvray
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 346
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Book Description
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
Author: Danail Bonchev
Publisher: Taylor & Francis
ISBN: 9780856265150
Category : Design
Languages : en
Pages : 294
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Book Description
Building on the background of graph theory provided in the first volume of the series, presents a detailed examination of the role of graph theory in the study of chemical kinetics, reaction mechanisms, and quantitative structure-activity relations, in a manner useful to theoretical chemists. Among the topics are heterogeneous catalytic reactions, the classification and coding of chemical reaction mechanisms, the mechanist's description of chemical processes as it relates to aromaticity, and using operator networks to interpret evolutionary interrelations between chemical entities. Annotation copyright by Book News, Inc., Portland, OR
Author: Aurora Clark
Publisher: Wiley
ISBN: 9781119794158
Category : Science
Languages : en
Pages : 0
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Book Description
An Advanced Textbook Introducing Graph Theory and Topological Data Analysis for Chemists Chemistry is at a tipping point where the integration with applied mathematics is dramatically expanding research paradigms, chemical models and theories. Methods that include graph theory, algebraic geometry, geometric topology and topological data analysis expand chemical insight by providing intuitive information extracted from complex chemistry data. Written by a world leader and pioneer in graph theory and topological analyses in chemistry, The Shape of Data in Chemistry is an advanced textbook that introduces the aforementioned topics to chemists so that they may identify patterns and correlations in data sets that span electronic structure, the statistical ensembles of molecules, colloids, and interfaces, as well as experimental measurement. Within detailed chapters that introduce core concepts and theoretical backgrounds, ‘real world’ examples are described that are supported by online data sets, Jupyter notebooks, and discussion on expanding chemistry concepts/models. Case study chapters are also presented throughout the text, highlighting applications of these methods in the study of chemical reaction networks, nanoporous materials, energy landscapes, and many others. Some of the topics and learning materials covered and included within the work are: Graph theory: descriptors of chemical graphs across scale, spectral graph theory, and dynamic properties of chemical graphs Topological data analysis: morse theory, topological spaces in chemistry, geometric measure theory, homology and persistence, stability and distance, and integration with machine learning A companion website hosts data sets and Jupyter notebooks to accompany the real-world examples and case studies presented throughout the book Example software input files for analyses with different codes are also included to aid in reader comprehension The Shape of Data in Chemistry serves as a forward-thinking and modern introduction to graph theory and topological analysis for researchers working at the intersection of chemistry, applied mathematics, and data science, as well as those in fields related to computational chemistry, materials science, physics and applied mathematics. Upper-level undergraduate and graduate students enrolled in courses that focus on data science in the physical sciences will also be able to use the work to gain an understanding of innovative topics related to their areas of study, while math students will find unique applications and domain expertise that inspire mathematical development.
