Topological Theory Of Graphs
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Topological Theory Of Graphs
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Author : Yanpei Liu
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-03-06
Topological Theory Of Graphs written by Yanpei Liu and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-06 with Mathematics categories.
This book introduces polyhedra as a tool for graph theory and discusses their properties and applications in solving the Gauss crossing problem. The discussion is extended to embeddings on manifolds, particularly to surfaces of genus zero and non-zero via the joint tree model, along with solution algorithms. Given its rigorous approach, this book would be of interest to researchers in graph theory and discrete mathematics.
Topics In Topological Graph Theory
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Author : Lowell W. Beineke
language : en
Publisher: Cambridge University Press
Release Date : 2009-07-09
Topics In Topological Graph Theory written by Lowell W. Beineke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-09 with Mathematics categories.
The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there are no other books with such a wide scope. This book contains fifteen expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory and the topology of surfaces. Each chapter concludes with an extensive list of references.
Topological Graph Theory
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Author : Jonathan L. Gross
language : en
Publisher: Courier Corporation
Release Date : 2001-01-01
Topological Graph Theory written by Jonathan L. Gross and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
Iintroductory treatment emphasizes graph imbedding but also covers connections between topological graph theory and other areas of mathematics. Authors explore the role of voltage graphs in the derivation of genus formulas, explain the Ringel-Youngs theorem, and examine the genus of a group, including imbeddings of Cayley graphs. Many figures. 1987 edition.
Topological Theory On Graphs
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Author : Yanpei Liu
language : en
Publisher:
Release Date : 2008
Topological Theory On Graphs written by Yanpei Liu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Graph theory categories.
The Foundations Of Topological Graph Theory
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Author : C.Paul Bonnington
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Foundations Of Topological Graph Theory written by C.Paul Bonnington and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is not a traditional work on topological graph theory. No current graph or voltage graph adorns its pages. Its readers will not compute the genus (orientable or non-orientable) of a single non-planar graph. Their muscles will not flex under the strain of lifting walks from base graphs to derived graphs. What is it, then? It is an attempt to place topological graph theory on a purely combinatorial yet rigorous footing. The vehicle chosen for this purpose is the con cept of a 3-graph, which is a combinatorial generalisation of an imbedding. These properly edge-coloured cubic graphs are used to classify surfaces, to generalise the Jordan curve theorem, and to prove Mac Lane's characterisation of planar graphs. Thus they playa central role in this book, but it is not being suggested that they are necessarily the most effective tool in areas of topological graph theory not dealt with in this volume. Fruitful though 3-graphs have been for our investigations, other jewels must be examined with a different lens. The sole requirement for understanding the logical development in this book is some elementary knowledge of vector spaces over the field Z2 of residue classes modulo 2. Groups are occasionally mentioned, but no expertise in group theory is required. The treatment will be appreciated best, however, by readers acquainted with topology. A modicum of topology is required in order to comprehend much of the motivation we supply for some of the concepts introduced.
Topological Field Theory Primitive Forms And Related Topics
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Author : A. Kashiwara
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topological Field Theory Primitive Forms And Related Topics written by A. Kashiwara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely. This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as a mathematical notion to define a "good period mapping" for a family of analytic structures. The invited papers in this volume are expository in nature by participants of the Taniguchi Symposium on "Topological Field Theory, Primitive Forms and Related Topics" and the RIMS Symposium bearing the same title, both held in Kyoto. The papers reflect the broad research of some of the world's leading mathematical physicists, and should serve as an excellent resource for researchers as well as graduate students of both disciplines.
Topological Field Theory Primitive Forms And Related Topics
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Author : Masaki Kashiwara
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-12
Topological Field Theory Primitive Forms And Related Topics written by Masaki Kashiwara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12 with Mathematics categories.
As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely. This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as a mathematical notion to define a "good period mapping" for a family of analytic structures. The invited papers in this volume are expository in nature by participants of the Taniguchi Symposium on "Topological Field Theory, Primitive Forms and Related Topics" and the RIMS Symposium bearing the same title, both held in Kyoto. The papers reflect the broad research of some of the world's leading mathematical physicists, and should serve as an excellent resource for researchers as well as graduate students of both disciplines.
Gateways Unveiling The Mysteries Of Topological Graph Theory
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-03-09
Gateways Unveiling The Mysteries Of Topological Graph Theory written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-09 with Mathematics categories.
Embark on a captivating journey through the world of topological graph theory, a captivating field that unveils the profound interplay between topology and graph theory. This comprehensive and engaging book offers a comprehensive exposition of the fundamental concepts, diverse applications, and recent advancements in topological graph theory, catering to a wide audience of mathematicians, computer scientists, and anyone fascinated by the intricate world of graphs and surfaces. Unravel the mysteries of graph imbeddings, delving into the intricate connections between graphs and surfaces. Explore the concept of genus, a captivating measure of the complexity of graph imbeddings, and uncover the profound implications of Ringel-Youngs theorem, a groundbreaking result that revolutionized the field of graph theory. Discover the wide-ranging applications of topological graph theory, spanning diverse fields such as computer science, network analysis, physics, and biology. Learn how topological graph theory empowers us to solve complex problems in network design, data analysis, and scientific modeling. Navigate through a wealth of captivating examples, illuminating figures, and thought-provoking exercises, all carefully crafted to enhance your understanding and deepen your appreciation for topological graph theory. Engage with the cutting-edge research and unsolved problems at the forefront of topological graph theory, gaining insights into the future directions and open challenges in this captivating field. Written with clarity and rigor, this book serves as an indispensable resource for mathematicians, computer scientists, and anyone seeking to delve into the captivating realm of topological graph theory. Whether you are a seasoned researcher, a budding student, or simply a curious explorer of the intricate world of graphs and networks, this book promises an enlightening and intellectually stimulating experience. If you like this book, write a review!
Applications Of Algebraic Topology
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Author : S. Lefschetz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applications Of Algebraic Topology written by S. Lefschetz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This monograph is based, in part, upon lectures given in the Princeton School of Engineering and Applied Science. It presupposes mainly an elementary knowledge of linear algebra and of topology. In topology the limit is dimension two mainly in the latter chapters and questions of topological invariance are carefully avoided. From the technical viewpoint graphs is our only requirement. However, later, questions notably related to Kuratowski's classical theorem have demanded an easily provided treatment of 2-complexes and surfaces. January 1972 Solomon Lefschetz 4 INTRODUCTION The study of electrical networks rests upon preliminary theory of graphs. In the literature this theory has always been dealt with by special ad hoc methods. My purpose here is to show that actually this theory is nothing else than the first chapter of classical algebraic topology and may be very advantageously treated as such by the well known methods of that science. Part I of this volume covers the following ground: The first two chapters present, mainly in outline, the needed basic elements of linear algebra. In this part duality is dealt with somewhat more extensively. In Chapter III the merest elements of general topology are discussed. Graph theory proper is covered in Chapters IV and v, first structurally and then as algebra. Chapter VI discusses the applications to networks. In Chapters VII and VIII the elements of the theory of 2-dimensional complexes and surfaces are presented.
Algebraic Elements Of Graphs
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Author : Yanpei Liu
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-09-11
Algebraic Elements Of Graphs written by Yanpei Liu and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-11 with Mathematics categories.
This book studies algebraic representations of graphs in order to investigate combinatorial structures via local symmetries. Topological, combinatorial and algebraic classifications are distinguished by invariants of polynomial type and algorithms are designed to determine all such classifications with complexity analysis. Being a summary of the author‘s original work on graph embeddings, this book is an essential reference for researchers in graph theory. Contents Abstract Graphs Abstract Maps Duality Orientability Orientable Maps Nonorientable Maps Isomorphisms of Maps Asymmetrization Asymmetrized Petal Bundles Asymmetrized Maps Maps within Symmetry Genus Polynomials Census with Partitions Equations with Partitions Upper Maps of a Graph Genera of a Graph Isogemial Graphs Surface Embeddability