Graphs Of Groups On Surfaces

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Graphs Groups And Surfaces

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Author : A.T. White
language : en
Publisher: Elsevier
Release Date : 1985-01-01

Graphs Groups And Surfaces written by A.T. White and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-01 with Mathematics categories.

The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'' and 9 as ``unsolved''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''.

Graphs Of Groups On Surfaces

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Author : A.T. White
language : en
Publisher: Elsevier
Release Date : 2001-04-27

Graphs Of Groups On Surfaces written by A.T. White and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-27 with Mathematics categories.

The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topological graph theory and random topological graph theory, as well as a chapter on the composition of English church-bell music. The latter is facilitated by imbedding the right graph of the right group on an appropriate surface, with suitable symmetries. Throughout the emphasis is on Cayley maps: imbeddings of Cayley graphs for finite groups as (possibly branched) covering projections of surface imbeddings of loop graphs with one vertex. This is not as restrictive as it might sound; many developments in topological graph theory involve such imbeddings.The approach aims to make all this interconnected material readily accessible to a beginning graduate (or an advanced undergraduate) student, while at the same time providing the research mathematician with a useful reference book in topological graph theory. The focus will be on beautiful connections, both elementary and deep, within mathematics that can best be described by the intuitively pleasing device of imbedding graphs of groups on surfaces.

Graphs On Surfaces

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Author : Joanna A. Ellis-Monaghan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-28

Graphs On Surfaces written by Joanna A. Ellis-Monaghan 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 2013-06-28 with Mathematics categories.

Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors illustrate the interdependency between duality, medial graphs and knots; how this interdependency is reflected in algebraic invariants of graphs and knots; and how it can be exploited to solve problems in graph and knot theory. Taking a constructive approach, the authors emphasize how generalized duals and related ideas arise by localizing classical constructions, such as geometric duals and Tait graphs, and then removing artificial restrictions in these constructions to obtain full extensions of them to embedded graphs. The authors demonstrate the benefits of these generalizations to embedded graphs in chapters describing their applications to graph polynomials and knots. Graphs on Surfaces: Dualities, Polynomials, and Knots also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knot theorists. Directed at those with some familiarity with basic graph theory and knot theory, this book is appropriate for graduate students and researchers in either area. Because the area is advancing so rapidly, the authors give a comprehensive overview of the topic and include a robust bibliography, aiming to provide the reader with the necessary foundations to stay abreast of the field. The reader will come away from the text convinced of advantages of considering these higher genus analogues of constructions of plane and abstract graphs, and with a good understanding of how they arise.

Algebraic Graph Theory

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Author : Ulrich Knauer
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-10-08

Algebraic Graph Theory written by Ulrich Knauer 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 2019-10-08 with Mathematics categories.

Graph models are extremely useful for a large number of applications as they play an important role as structuring tools. They allow to model net structures – like roads, computers, telephones, social networks – instances of abstract data structures – like lists, stacks, trees – and functional or object oriented programming. The focus of this highly self-contained book is on homomorphisms and endomorphisms, matrices and eigenvalues.

Automorphisms Of Riemann Surfaces Subgroups Of Mapping Class Groups And Related Topics

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Author : Aaron Wootton
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-03

Automorphisms Of Riemann Surfaces Subgroups Of Mapping Class Groups And Related Topics written by Aaron Wootton and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-03 with Mathematics categories.

Automorphism groups of Riemann surfaces have been widely studied for almost 150 years. This area has persisted in part because it has close ties to many other topics of interest such as number theory, graph theory, mapping class groups, and geometric and computational group theory. In recent years there has been a major revival in this area due in part to great advances in computer algebra systems and progress in finite group theory. This volume provides a concise but thorough introduction for newcomers to the area while at the same time highlighting new developments for established researchers. The volume starts with two expository articles. The first of these articles gives a historical perspective of the field with an emphasis on highly symmetric surfaces, such as Hurwitz surfaces. The second expository article focuses on the future of the field, outlining some of the more popular topics in recent years and providing 78 open research problems across all topics. The remaining articles showcase new developments in the area and have specifically been chosen to cover a variety of topics to illustrate the range of diversity within the field.

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.

Groups Acting On Graphs

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Author : Warren Dicks
language : en
Publisher: Cambridge University Press
Release Date : 1989-03-09

Groups Acting On Graphs written by Warren Dicks 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 1989-03-09 with Mathematics categories.

Originally published in 1989, this is an advanced text and research monograph on groups acting on low-dimensional topological spaces, and for the most part the viewpoint is algebraic. Much of the book occurs at the one-dimensional level, where the topology becomes graph theory. Two-dimensional topics include the characterization of Poincare duality groups and accessibility of almost finitely presented groups. The main three-dimensional topics are the equivariant loop and sphere theorems. The prerequisites grow as the book progresses up the dimensions. A familiarity with group theory is sufficient background for at least the first third of the book, while the later chapters occasionally state without proof and then apply various facts which require knowledge of homological algebra and algebraic topology. This book is essential reading for anyone contemplating working in the subject.

Finite Groups 72

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Author : Terrence Gagen
language : en
Publisher:
Release Date : 1973

Finite Groups 72 written by Terrence Gagen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Finite groups categories.

Automorphism Groups Of Maps Surfaces And Smarandache Geometries Second Edition Graduate Text Book In Mathematics

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Author : Linfan Mao
language : en
Publisher: Infinite Study
Release Date : 2011

Automorphism Groups Of Maps Surfaces And Smarandache Geometries Second Edition Graduate Text Book In Mathematics written by Linfan Mao and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Automorphisms categories.

Introductory Graph Theory

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Author : Gary Chartrand
language : en
Publisher: Courier Corporation
Release Date : 2012-04-30

Introductory Graph Theory written by Gary Chartrand and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-30 with Science categories.

Clear, lively style covers all basics of theory and application, including mathematical models, elementary graph theory, transportation problems, connection problems, party problems, diagraphs and mathematical models, games and puzzles, more.