The Foundations of Topological Graph Theory

The Foundations of Topological Graph Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 179
Release :
ISBN-10 : 9781461225409
ISBN-13 : 146122540X
Rating : 4/5 (40X Downloads)

Book Synopsis The Foundations of Topological Graph Theory by : C.Paul Bonnington

Download or read book The Foundations of Topological Graph Theory written by C.Paul Bonnington and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


The Foundations of Topological Graph Theory Related Books

The Foundations of Topological Graph Theory
Language: en
Pages: 179
Authors: C.Paul Bonnington
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

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 (orientab
Topics in Topological Graph Theory
Language: en
Pages:
Authors: Lowell W. Beineke
Categories: Mathematics
Type: BOOK - Published: 2009-07-09 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

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 mat
Topological Graph Theory
Language: en
Pages: 386
Authors: Jonathan L. Gross
Categories: Mathematics
Type: BOOK - Published: 2001-01-01 - Publisher: Courier Corporation

DOWNLOAD EBOOK

Iintroductory treatment emphasizes graph imbedding but also covers connections between topological graph theory and other areas of mathematics. Authors explore
Topological Theory of Graphs
Language: en
Pages: 369
Authors: Yanpei Liu
Categories: Mathematics
Type: BOOK - Published: 2017-03-06 - Publisher: Walter de Gruyter GmbH & Co KG

DOWNLOAD EBOOK

This book introduces polyhedra as a tool for graph theory and discusses their properties and applications in solving the Gauss crossing problem. The discussion
Mathematical Foundations of Network Analysis
Language: en
Pages: 205
Authors: Paul Slepian
Categories: Science
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

In this book we attempt to develop the fundamental results of resistive network analysis, based upon a sound mathematical structure. The axioms upon which our d