The Foundations of Topological Graph Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Foundations of Topological Graph Theory write by C.Paul Bonnington. This book was released on 2012-12-06. The Foundations of Topological Graph Theory available in PDF, EPUB and Kindle. 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.
Graph Theory and Its Applications, Second Edition
Graph Theory and Its Applications, Second Edition - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Graph Theory and Its Applications, Second Edition write by Jonathan L. Gross. This book was released on 2005-09-22. Graph Theory and Its Applications, Second Edition available in PDF, EPUB and Kindle. Already an international bestseller, with the release of this greatly enhanced second edition, Graph Theory and Its Applications is now an even better choice as a textbook for a variety of courses -- a textbook that will continue to serve your students as a reference for years to come. The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine. What else is new? New chapters on measurement and analytic graph theory Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing. Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of reader Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.
Topics in Topological Graph Theory
Topics in Topological Graph Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topics in Topological Graph Theory write by Lowell W. Beineke. This book was released on 2009-07-09. Topics in Topological Graph Theory available in PDF, EPUB and Kindle. 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.
Evasiveness of Graph Properties and Topological Fixed-Point Theorems
Evasiveness of Graph Properties and Topological Fixed-Point Theorems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Evasiveness of Graph Properties and Topological Fixed-Point Theorems write by Carl A. Miller. This book was released on 2013. Evasiveness of Graph Properties and Topological Fixed-Point Theorems available in PDF, EPUB and Kindle. Evasiveness of Graph Properties and Topological Fixed-Point Theorems provides the reader with an integrated treatment of the underlying proofs in the body of research around the use of topological methods to prove lower bounds on the complexity of graph properties.
Elementary Concepts of Topology
Elementary Concepts of Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elementary Concepts of Topology write by Paul Alexandroff. This book was released on 2012-08-13. Elementary Concepts of Topology available in PDF, EPUB and Kindle. Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.
