The Foundations Of Topological Graph Theory

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The Foundations of Topological Graph Theory

Author : C.Paul Bonnington
Publisher : Springer Science & Business Media
ISBN 13 : 146122540X
Total Pages : 179 pages
Book Rating : 4.4/5 (612 download)

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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.

Topics in Topological Graph Theory

Author : Lowell W. Beineke
Publisher : Cambridge University Press
ISBN 13 : 1139643681
Total Pages : pages
Book Rating : 4.1/5 (396 download)

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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 and published by Cambridge University Press. This book was released on 2009-07-09 with total page pages. 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.

Topological Graph Theory

Author : Jonathan L. Gross
Publisher : Courier Corporation
ISBN 13 : 0486417417
Total Pages : 386 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Topological Graph Theory by : Jonathan L. Gross

Download or read book Topological Graph Theory written by Jonathan L. Gross and published by Courier Corporation. This book was released on 2001-01-01 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 of Graphs

Author : Yanpei Liu
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110479494
Total Pages : 369 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Topological Theory of Graphs by : Yanpei Liu

Download or read book Topological Theory of Graphs written by Yanpei Liu and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-03-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Foundations of Network Analysis

Author : Paul Slepian
Publisher : Springer Science & Business Media
ISBN 13 : 364287424X
Total Pages : 205 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Mathematical Foundations of Network Analysis by : Paul Slepian

Download or read book Mathematical Foundations of Network Analysis written by Paul Slepian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 development is based are Ohm's Law, Kirchhoff's Voltage Law, and Kirchhoff's Current Law. In order to state these axioms precisely, and use them in the development of our network analysis, an elaborate mathematical structure is introduced, involving concepts of graph theory, linear algebra, and one dimensional algebraic topology. The graph theory and one dimensional algebraic topology used are developed from first principles; the reader needs no background in these subjects. However, we do assume that the reader has some familiarity with elementary linear algebra. It is now stylish to teach elementary linear algebra at the sophomore college level, and we feel that the require ment that the reader should be familiar with elementary linear algebra is no more demanding than the usual requirement in most electrical engineering texts that the reader should be familiar with calculus. In this book, however, no calculus is needed. Although no formal training in circuit theory is needed for an understanding of the book, such experience would certainly help the reader by presenting him with familiar examples relevant to the mathematical abstractions introduced. It is our intention in this book to exhibit the effect of the topological properties of the network upon the branch voltages and branch currents, the objects of interest in network analysis.

The Four-Color Theorem

Author : Rudolf Fritsch
Publisher : Springer Science & Business Media
ISBN 13 : 1461217202
Total Pages : 269 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Four-Color Theorem by : Rudolf Fritsch

Download or read book The Four-Color Theorem written by Rudolf Fritsch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map so that no two adjoining countries have the same color? This problem remained unsolved until the 1950s, when it was finally cracked using a computer. This book discusses the history and mathematics of the problem, as well as the philosophical debate which ensued, regarding the validity of computer generated proofs.

Graphs on Surfaces

Author : Joanna A. Ellis-Monaghan
Publisher : Springer Science & Business Media
ISBN 13 : 1461469716
Total Pages : 139 pages
Book Rating : 4.4/5 (614 download)

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

Download or read book Graphs on Surfaces written by Joanna A. Ellis-Monaghan and published by Springer Science & Business Media. This book was released on 2013-06-28 with total page 139 pages. 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.

Quantitative Graph Theory

Author : Matthias Dehmer
Publisher : CRC Press
ISBN 13 : 1466584513
Total Pages : 530 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Quantitative Graph Theory by : Matthias Dehmer

Download or read book Quantitative Graph Theory written by Matthias Dehmer and published by CRC Press. This book was released on 2014-10-27 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as: Comparative approaches (graph similarity or distance) Graph measures to characterize graphs quantitatively Applications of graph measures in social network analysis and other disciplines Metrical properties of graphs and measures Mathematical properties of quantitative methods or measures in graph theory Network complexity measures and other topological indices Quantitative approaches to graphs using machine learning (e.g., clustering) Graph measures and statistics Information-theoretic methods to analyze graphs quantitatively (e.g., entropy) Through its broad coverage, Quantitative Graph Theory: Mathematical Foundations and Applications fills a gap in the contemporary literature of discrete and applied mathematics, computer science, systems biology, and related disciplines. It is intended for researchers as well as graduate and advanced undergraduate students in the fields of mathematics, computer science, mathematical chemistry, cheminformatics, physics, bioinformatics, and systems biology.

Handbook of Graph Theory

Author : Jonathan L. Gross
Publisher : CRC Press
ISBN 13 : 1439880190
Total Pages : 1606 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Handbook of Graph Theory by : Jonathan L. Gross

Download or read book Handbook of Graph Theory written by Jonathan L. Gross and published by CRC Press. This book was released on 2013-12-17 with total page 1606 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition-over 400 pages longer than its prede

Applied Graph Theory

Author : Wai-Kai Chen
Publisher : Elsevier
ISBN 13 : 1483164152
Total Pages : 558 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Applied Graph Theory by : Wai-Kai Chen

Download or read book Applied Graph Theory written by Wai-Kai Chen and published by Elsevier. This book was released on 2014-11-28 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Graph Theory: Graphs and Electrical Networks, Second Revised Edition provides a concise discussion of the fundamentals of graph and its application to the electrical network theory. The book emphasizes the mathematical precision of the concepts and principles involved. The text first covers the basic theory of graph, and then proceeds to tackling in the next three chapters the various applications of graph to electrical network theory. These chapters also discuss the foundations of electrical network theory; directed-graph solutions of linear algebraic equations; and topological analysis of linear systems. Next, the book covers trees and their generation. Chapter 6 deals with the realizability of directed graphs with prescribed degrees, while Chapter 7 talks about state equations of networks. The book will be of great use to researchers of network topology, linear systems, and circuitries.

Graphs of Groups on Surfaces

Author : A.T. White
Publisher : Elsevier
ISBN 13 : 0080507581
Total Pages : 378 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Graphs of Groups on Surfaces by : A.T. White

Download or read book Graphs of Groups on Surfaces written by A.T. White and published by Elsevier. This book was released on 2001-04-27 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Graph Theory

Author : Ulrich Knauer
Publisher : Walter de Gruyter
ISBN 13 : 311025509X
Total Pages : 325 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Algebraic Graph Theory by : Ulrich Knauer

Download or read book Algebraic Graph Theory written by Ulrich Knauer and published by Walter de Gruyter. This book was released on 2011-09-29 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph models are extremely useful for almost all applications and applicators as they play an important role as structuring tools. They allow to model net structures – like roads, computers, telephones – instances of abstract data structures – like lists, stacks, trees – and functional or object oriented programming. In turn, graphs are models for mathematical objects, like categories and functors. This highly self-contained book about algebraic graph theory is written with a view to keep the lively and unconventional atmosphere of a spoken text to communicate the enthusiasm the author feels about this subject. The focus is on homomorphisms and endomorphisms, matrices and eigenvalues. It ends with a challenging chapter on the topological question of embeddability of Cayley graphs on surfaces.

Using the Mathematics Literature

Author : Kristine K. Fowler
Publisher : CRC Press
ISBN 13 : 9780824750350
Total Pages : 412 pages
Book Rating : 4.7/5 (53 download)

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Book Synopsis Using the Mathematics Literature by : Kristine K. Fowler

Download or read book Using the Mathematics Literature written by Kristine K. Fowler and published by CRC Press. This book was released on 2004-05-25 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.

Fundamentals of Graph Theory

Author : Allan Bickle
Publisher : American Mathematical Soc.
ISBN 13 : 1470453428
Total Pages : 336 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Fundamentals of Graph Theory by : Allan Bickle

Download or read book Fundamentals of Graph Theory written by Allan Bickle and published by American Mathematical Soc.. This book was released on 2020-03-10 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is a fascinating and inviting branch of mathematics. Many problems are easy to state and have natural visual representations, inviting exploration by new students and professional mathematicians. The goal of this textbook is to present the fundamentals of graph theory to a wide range of readers. The book contains many significant recent results in graph theory, presented using up-to-date notation. The author included the shortest, most elegant, most intuitive proofs for modern and classic results while frequently presenting them in new ways. Major topics are introduced with practical applications that motivate their development, and which are illustrated with examples that show how to apply major theorems in practice. This includes the process of finding a brute force solution (case-checking) when an elegant solution is not apparent. With over 1200 exercises, internet resources (e.g., the OEIS for counting problems), helpful appendices, and a detailed guide to different course outlines, this book provides a versatile and convenient tool for the needs of instructors at a large variety of institutions.

Graph Drawing

Author : Ulrik Brandes
Publisher : Springer Science & Business Media
ISBN 13 : 3642184685
Total Pages : 425 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Graph Drawing by : Ulrik Brandes

Download or read book Graph Drawing written by Ulrik Brandes and published by Springer Science & Business Media. This book was released on 2011-01-14 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the refereed proceedings of the 18th International Symposium on Graph Drawing, GD 2010, held in Konstanz, Germany, during September 2010. The 30 revised full papers presented together with 5 revised short and 8 poster papers were carefully reviewed and selected from 77 submissions. The volume also contains a detailed report about the 17th Annual Graph Drawing Contest, held as a satellite event of GD 2010. Devoted both to theoretical advances as well as to implemented solutions, the papers are concerned with the geometric representation of graphs and networks and are motivated by those applications where it is crucial to visualize structural information as graphs.

Multidisciplinary Approach in Arts, Science & Commerce (Volume-1)

Author : BIPLAB AUDDYA
Publisher : Sankalp Publication
ISBN 13 : 9394901256
Total Pages : 114 pages
Book Rating : 4.3/5 (949 download)

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Book Synopsis Multidisciplinary Approach in Arts, Science & Commerce (Volume-1) by : BIPLAB AUDDYA

Download or read book Multidisciplinary Approach in Arts, Science & Commerce (Volume-1) written by BIPLAB AUDDYA and published by Sankalp Publication. This book was released on with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multidisciplinary Approach/Research/Subject/Education is a unique part of education. By this education students learn and collect knowledge/ideas from different disciplines. The present E-Book volume is based on the Multidisciplinary Research and introduces on different important topics by research paper contributors like: Awareness towards contraceptive use among rural and urban couples, Health problems of tribal community, Health Problems of Women in Tribal Society, Discovery of patterns from web page navigation sequences in datamining, DATA PERTURBATION USING LAPLACE NOISE, DATA PERTURBATION USING LAPLACE NOISE, ANALYSIS OF RVD BASED ON THE CART DERIVED TREE ALGORITHM, Comparative study to assess the awareness towards post-menopausal life among rural & urban women, Informal Trade in the Northeast and its Relation to Interpersonal Contact, Comparative study to assess the barriers towards contraceptive use among rural & urban couples, Awareness towards post-menopausal life among urban women in community setting, Attributes Of Product Outlook That Influence Purchases Of Two-Wheelers by Women Consumers, Preparation of Safe Anti Rust Polish And Rust Removing Pad for Preventing Stainless Steel Sheets in Iron Steel Industry, Fruit Processing Industry in India: A Case of Kingberry Strawberry Wine, Maharashtra, A Review on Applications of Blockchain Technology in Banking and Financial Sector, Fuzzy Transportation problem using Topologized Graphical Method, A REVIEW ON ETHNOMEDICINAL, PHYTOCHEMICAL, PHYTOPHARMACOLOGICAL AND COLORING POTENTIAL OF Lawsonia inermis L.(Henna), Development in Teaching and Learning process through ICT. Thanks to Sankalp Publication, all Editors (Dr. P. PRABAKARAN, Dr. R. SHALINI, Dr. S. NAGASUNDARAM & DR. SHERIN SARA KOSHY), all Co-Editors (MD SAHIDUL AREFIN, DR. GITTY GEORGE, DR. K. S. SRIDEVI SANGEETA & D R K SAIKANTH) and all Research Paper Contributors of this E-Book.

Graph Algorithms and Applications 2

Author : Giuseppe Liotta
Publisher : World Scientific
ISBN 13 : 9812388559
Total Pages : 534 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Graph Algorithms and Applications 2 by : Giuseppe Liotta

Download or read book Graph Algorithms and Applications 2 written by Giuseppe Liotta and published by World Scientific. This book was released on 2004 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains Volumes 4 and 5 of the Journal of Graph Algorithms and Applications (JGAA). The first book of this series, Graph Algorithms and Applications I, published in March 2002, contains Volumes 1-3 of JGAA. JGAA is a peer-reviewed scientific journal devoted to the publication of high-quality research papers on the analysis, design, implementation, and applications of graph algorithms. Areas of interest include computational biology, computational geometry, computer graphics, computer-aided design, computer and interconnection networks, constraint systems, databases, graph drawing, graph embedding and layout, knowledge representation, multimedia, software engineering, telecommunications networks, user interfaces and visualization, and VLSI circuit design. The journal is supported by distinguished advisory and editorial boards, has high scientific standards, and takes advantage of current electronic document technology. The electronic version of JGAA is available on the Web at http: //www.cs.brown.edu/publications/jgaa/. Graph Algorithms and Applications 2 presents contributions from prominent authors and includes selected papers from the Dagstuhl Seminar on Graph Algorithms and Applications and the Symposium on Graph Drawing in 1998. All papers in the book have extensive diagrams and offer a unique treatment of graph algorithms focusing on the important applications.