Share

Graphs on Surfaces and Their Applications

2013-04-17 Mathematics
Download Graphs on Surfaces and Their Applications PDF Online Free

Author :
Release : 2013-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 611/5 ( reviews)

GET EBOOK


Book Synopsis Graphs on Surfaces and Their Applications by : Sergei K. Lando

Download or read book Graphs on Surfaces and Their Applications written by Sergei K. Lando. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.

Graphs on Surfaces

2001-08-02 Mathematics
Download Graphs on Surfaces PDF Online Free

Author :
Release : 2001-08-02
Genre : Mathematics
Kind : eBook
Book Rating : 890/5 ( reviews)

GET EBOOK


Book Synopsis Graphs on Surfaces by : Bojan Mohar

Download or read book Graphs on Surfaces written by Bojan Mohar. This book was released on 2001-08-02. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is one of the fastest growing branches of mathematics. Until recently, it was regarded as a branch of combinatorics and was best known by the famous four-color theorem stating that any map can be colored using only four colors such that no two bordering countries have the same color. Now graph theory is an area of its own with many deep results and beautiful open problems. Graph theory has numerous applications in almost every field of science and has attracted new interest because of its relevance to such technological problems as computer and telephone networking and, of course, the internet. In this new book in the Johns Hopkins Studies in the Mathematical Science series, Bojan Mohar and Carsten Thomassen look at a relatively new area of graph theory: that associated with curved surfaces. Graphs on surfaces form a natural link between discrete and continuous mathematics. The book provides a rigorous and concise introduction to graphs on surfaces and surveys some of the recent developments in this area. Among the basic results discussed are Kuratowski's theorem and other planarity criteria, the Jordan Curve Theorem and some of its extensions, the classification of surfaces, and the Heffter-Edmonds-Ringel rotation principle, which makes it possible to treat graphs on surfaces in a purely combinatorial way. The genus of a graph, contractability of cycles, edge-width, and face-width are treated purely combinatorially, and several results related to these concepts are included. The extension by Robertson and Seymour of Kuratowski's theorem to higher surfaces is discussed in detail, and a shorter proof is presented. The book concludes with a survey of recent developments on coloring graphs on surfaces.

Graphs on Surfaces

2013-06-28 Mathematics
Download Graphs on Surfaces PDF Online Free

Author :
Release : 2013-06-28
Genre : Mathematics
Kind : eBook
Book Rating : 716/5 ( reviews)

GET EBOOK


Book Synopsis Graphs on Surfaces by : Joanna A. Ellis-Monaghan

Download or read book Graphs on Surfaces written by Joanna A. Ellis-Monaghan. This book was released on 2013-06-28. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Research Topics in Graph Theory and Its Applications

2019-06-24 Mathematics
Download Research Topics in Graph Theory and Its Applications PDF Online Free

Author :
Release : 2019-06-24
Genre : Mathematics
Kind : eBook
Book Rating : 289/5 ( reviews)

GET EBOOK


Book Synopsis Research Topics in Graph Theory and Its Applications by : Vadim Zverovich

Download or read book Research Topics in Graph Theory and Its Applications written by Vadim Zverovich. This book was released on 2019-06-24. Available in PDF, EPUB and Kindle. Book excerpt: This book considers a number of research topics in graph theory and its applications, including ideas devoted to alpha-discrepancy, strongly perfect graphs, reconstruction conjectures, graph invariants, hereditary classes of graphs, and embedding graphs on topological surfaces. It also discusses applications of graph theory, such as transport networks and hazard assessments based on unified networks. The book is ideal for developers of grant proposals and researchers interested in exploring new areas of graph theory and its applications.

Topics in Topological Graph Theory

2009-07-09 Mathematics
Download Topics in Topological Graph Theory PDF Online Free

Author :
Release : 2009-07-09
Genre : Mathematics
Kind : eBook
Book Rating : 681/5 ( reviews)

GET EBOOK


Book Synopsis Topics in Topological Graph Theory by : Lowell W. Beineke

Download or read book Topics in Topological Graph Theory written by Lowell W. Beineke. This book was released on 2009-07-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

You may also like...